fix_rigid_example.pdf

D. Keffer, MSE 614, Dept. of Materials Science & Engineering, University of Tennessee, Knoxville
1
Rigid Dynamics in LAMMPS
David Keffer
Department of Materials Science & Engineering
University of Tennessee, Knoxville
date begun: March 8, 2016
date last updated: March 22, 2016
Table of Contents
I. Purpose of Document ........................................................................................................... 2
II. Review of Rigid Body Dynamics........................................................................................ 2
III. Simulation of Rigid Molecules.......................................................................................... 4
III.A. Simulation of a Single Carbon Dioxide Molecule..................................................... 4
III.B. Simulation of a System of Carbon Dioxide Molecules.............................................. 5
Appendix A. Carbon Dioxide: config_co2_1.txt ....................................................... 6
Appendix B. Carbon Dioxide: input_co2_1.txt.......................................................... 7
Appendix C. Carbon Dioxide: input_co2_sys.txt..................................................... 8
Appendix D. Carbon Dioxide: config_co2_sys.txt ................................................ 10

2
I. Purpose of Document
The purpose of this document is to provide a practical introduction to the simulation of rigid
molecules in LAMMPS. This is useful, for example, with molecules like carbon dioxide, which
have high vibrational frequencies for the C=O bonds. To simulate the flexible system requires a
very small time step. Often the approximation of the molecule as a rigid body is sufficient to
capture the physics of interest and offers a significant computational savings.
II. Review of Rigid Body Dynamics
We consider a molecule with Napm atoms per molecule. Each atom has a position, ri, and
velocity, vi, in the “laboratory frame of reference”.
The dynamics of a rigid body are divided into translation of the center of mass and rotation
about the center of mass. Each molecule has a center of mass position, defined as
∑
∑
=
=
≡ apm
apm
N
i
i
N
i
i
i
m
m
1
1
com
r
R (1)
The velocity of the center of mass of a molecule
∑
∑
∑
∑
=
=
=
=
=
=
≡ apm
apm
apm
apm
N
i
i
N
i
i
i
N
i
i
N
i
i
i
m
m
m
dt
d
m
dt
d
1
1
1
1
com
com
v
r
R
v (2)
The acceleration of the center of mass of a molecule
com
com
com
1
1
1
1
1
1
1
com
com
1
1
f
f
f
a
v
v
a
m
m
m
m
m
m
dt
d
m
dt
d
apm
apm
apm
apm
apm
apm
apm
N
i
i
N
i
i
N
i
i
N
i
i
N
i
i
i
N
i
i
N
i
i
i
=
=
=
=
=
≡
∑
∑
∑
∑
∑
∑
∑
=
=
=
=
=
=
=
(3)
where we have invoked Newton’s equation of motion, i
i
i m a
f = , on a particle basis. This
motion of the center of mass constitutes the translational degrees of freedom of the molecule.

3
We observe that the trajectory of the center of mass can be obtained based upon the forces
evaluated at each atomic position, something that LAMMPS is well suited to evaluate.
To describe the rotational degrees of freedom, we must define the torque on the rigid body,
( ) i
N
i
i
apm
f
R
r
T ×
−
≡ ∑
=1
com
com (4)
Again we note that the torque about the center of mass is entirely defined by the point positions
and forces. The moment of inertia of a set of points about their center of mass is defined as
∑
=
−
≡
apm
N
i
i
i
m
I
1
2
com
com R
r (5)
Newton’s second law for rotational dynamics relates the torque to the angular acceleration,
α , and the angular velocity, ω .
ω
ω
α com
com
com I
I ×
+
=
T (6)
The angular velocity of a rigid object is the same for all points and can thus be evaluated from
any single point be evaluated
( )
2
com
com
R
r
v
R
r
−
×
−
=
i
i
i
ω (7)
These equations thus provide the angular acceleration and angular velocity based on knowledge
of the point positions, velocities and forces. The acceleration of any point on the rigid object is
given by
( ) ( )
( ) com
com
com a
R
r
R
r +
−
×
×
+
−
×
= i
i
i
a ω
ω
a (8)
The kinetic energy of the rigid body has translation and rotational components
rot
tran KE
KE
KE +
= (9)

4
where
2
2
1
com
com
tran m
KE v
= (10)
2
2
1
ω
com
rot I
KE = (11)
For a nonlinear molecule translating and rotating in three-dimensional space, each of these
motions contains three degrees of freedom. The molecule can translate in the x, y and z
dimensions. The molecule can rotate about the x, y and z axes. Therefore according to the
equipartition theorem,
kT
KE
KE rot
tran
2
3
=
= (12)
Note that the kinetic energy of the system if all atoms were treated independently is
kT
N
m
KE apm
N
i
i
i
ind
apm
2
3
2
1
1
2
=
= ∑
=
v (13)
This is a totally different quantity. One consequence of this is that the LAMMPS command
for creating initial velocities for particles sets them to a specific temperature based on the
assumption of indpendence (equation (13)). Therefore, if the system is actually composed of
rigid bodies, the initial temperature based on this approach will be wrong for both the translation
and rotational degrees of freedom. To my knowledge, LAMMPS does not have a way to create
correct initial velocities corresponding to a set point temperature for rigid bodies.
III. Simulation of Rigid Molecules
In this section we first simulate a single molecule of carbon dioxide, then we simulate a
system of carbon dioxide molecules.
III.A. Simulation of a Single Carbon Dioxide Molecule

5
An initial configuration for a single carbon dioxide, CO2, molecule is given in Appendix A
config_co2_1.txt. The input configuration has 3 atoms of 2 types (C & O), 2 bonds of
one type (C=O), and 1 angle of 1 type (O=C=O). Importantly, the distance between atoms
corresponds to the equilibrium bond distance, which will not vary during the simulation since the
molecule is rigid. In other words, you should make sure that your input configuration is
consistent with the rigid potential.
A LAMMPS input file is given in Appendix B, input_co2_1.txt. This input file must
provide a fake (unused) bond force constant for the bond and angle modes. Here, we input a
value of 999.9 to emphasize the artificiality of these numbers. This code runs.
III.B. Simulation of a System of Carbon Dioxide Molecules
We next simulate a system of 125 carbon dioxide molecules. T LAMMPS input file is given
in Appendix C, input_co2_sys.txt. An initial configuration for a single carbon dioxide,
CO2, molecule is given in Appendix D, config_co2_sys.txt.
Six different fix commands are given invoking the rigid and rigid/small functionality. Of
these only four function when compute commands are present to calculate the translation kinetic
energy (ke/rigid) and rotational kinetic energy (erotate). The other two (rigid/nve/small and
rigid/nvt/small) cause segmentation faults.
For any of these fixes, there appear to be two serious problems. First, the temperature is not
the set point temperature. Of course, the initial velocity command can generate the correct initial
temperature for a fully flexible system, not a set of rigid objects. There are several suggestions
on the LAMMPS website for manipulating the input file to get the correct temperature, but we
found that none of these suggestions delivered the correct set point temperature at the initial
configuration.
Second, for none of the cases is the equipartition theorem satisfied. The sum of the
translational and rotational kinetic energies do not sum to 5/2NkT, as they should.
kT
N
KE
KE molec
rot
tran
2
5
=
+ (14)
We have 5 degrees of freedom here, corresponding to three degrees of translational freedom and
2 degrees of rotational freedom for a linear molecule, like CO2.
Thus, there remains serious reservations in using the rigid command in LAMMPS. For those
that believe that errors, which are not visible in other properties, are okay, proceed with caution.

6
Appendix A. Carbon Dioxide: config_co2_1.txt
LAMMPS INPUT FILE FOR co2_1
3 atoms
2 bonds
1 angles
0 dihedrals
0 impropers
2 atom types
1 bond types
1 angle types
0 dihedral types
0 improper types
-0.50000000E+02 0.50000000E+02 xlo xhi
-0.50000000E+02 0.50000000E+02 ylo yhi
-0.50000000E+02 0.50000000E+02 zlo zhi
Masses
1 0.12010700E+02
2 0.15999000E+02
Atoms
1 1 2 -0.35000000E+00 -0.11600000E+01 0.00000000E+00 0.00000000E+00 # O
2 1 1 0.70000000E+00 0.00000000E+00 0.00000000E+00 0.00000000E+00 # C
3 1 2 -0.35000000E+00 0.11600000E+01 0.00000000E+00 0.00000000E+00 # O
Bonds
1 1 1 2
2 1 2 3
Angles
1 1 1 2 3

7
Appendix B. Carbon Dioxide: input_co2_1.txt
#
units real
boundary p p p
atom_style full
read_data config_co2_1.txt
# interaction styles
pair_style lj/cut/coul/cut 12.0
bond_style harmonic
angle_style harmonic
pair_modify mix geometric tail yes
# force field parameters
# missing nonbonded parameters are inferred from mixing.
pair_coeff 1 1 0.0537 2.80 # C of CO2 ( 27 K = 0.0537 kcal/mol)
pair_coeff 2 2 0.1570 3.05 # O of CO2 (79 K = 0.1570 kcal/mol)
bond_coeff 1 999.9 1.16 # C=O (999.9 = fake number since not used)
angle_coeff 1 999.9 180.0 # O=C=O (999.9 = fake number since not used)
group all_co2 id <> 1 3
fix 1 all_co2 rigid/nve molecule # my_ketran = finite number
compute my_ketran all_co2 ke/rigid 1
compute my_kerot all_co2 erotate/rigid 1
compute my_temp all_co2 temp
timestep 1.0
reset_timestep 0
neigh_modify every 10 delay 20 check yes
thermo 500
thermo_style custom step c_my_ketran c_my_kerot temp c_my_temp pe ebond eangle
dump 1 all atom 100 dump.lammpstrj
run 0

8
Appendix C. Carbon Dioxide: input_co2_sys.txt
#
units real
boundary p p p
atom_style full
read_data config_co2_sys.txt
# interaction styles
pair_style lj/cut/coul/cut 12.0
bond_style harmonic
angle_style harmonic
pair_modify mix geometric tail yes
# force field parameters
# missing nonbonded parameters are inferred from mixing.
pair_coeff 1 1 0.0537 2.80 # C of CO2 ( 27 K = 0.0537 kcal/mol)
pair_coeff 2 2 0.1570 3.05 # O of CO2 (79 K = 0.1570 kcal/mol)
bond_coeff 1 999.9 1.16 # C=O (999.9 = fake number since not used)
angle_coeff 1 999.9 180.0 # O=C=O (999.9 = fake number since not used)
velocity all create 100.0 53244 dist gaussian mom no rot no
group clump id <> 1 375
#fix 1 clump rigid/small molecule # my_ketran = finite number
#fix 1 clump rigid/nve/small molecule # doesn't work with computing ke for rigid objects - Segmentation fault
#fix 1 clump rigid/nvt/small molecule temp 100.0 100.0 100.0 # doesn't work with computing ke for rigid objects -
Segmentation fault
#fix 1 clump rigid molecule # my_ketran = finite number
fix 1 clump rigid/nve molecule # my_ketran = finite number
#fix 1 clump rigid/nvt molecule temp 100.0 100.0 100.0 # my_ketran = finite number
compute my_ketran clump ke/rigid 1
compute my_kerot clump erotate/rigid 1
compute my_temp clump temp
##minimize 1.0e-4 1.0e-6 100 1000
timestep 1.0
reset_timestep 0
neigh_modify every 10 delay 20 check yes
thermo 500

9
#thermo_style multi
thermo_style custom step c_my_ketran c_my_kerot temp c_my_temp pe ebond eangle
dump 1 all atom 100 dump.lammpstrj
run 0

10
Appendix D. Carbon Dioxide: config_co2_sys.txt
LAMMPS INPUT FILE FOR co2_system
375 atoms
250 bonds
125 angles
0 dihedrals
0 impropers
2 atom types
1 bond types
1 angle types
0 dihedral types
0 improper types
0.0000000E+00 100.000000000000 xlo xhi
0.0000000E+00 100.000000000000 ylo yhi
0.0000000E+00 100.000000000000 zlo zhi
Masses
1 12.0107000000000
2 15.9990000000000
Atoms
1 1 2 -0.3500000E+00 0.8355413E+00 -0.8046557E+00 -0.2285103E-05
2 1 1 0.7000000E+00 0.0000000E+00 0.0000000E+00 0.0000000E+00
3 1 2 -0.3500000E+00 -0.8355413E+00 0.8046557E+00 0.2285103E-05
4 2 2 -0.3500000E+00 -0.7077159E+00 -0.3379484E+00 0.1914529E+02
5 2 1 0.7000000E+00 0.0000000E+00 0.0000000E+00 0.2000000E+02
6 2 2 -0.3500000E+00 0.7077159E+00 0.3379484E+00 0.2085471E+02
7 3 2 -0.3500000E+00 -0.5723737E+00 -0.3224989E+00 0.4095602E+02
8 3 1 0.7000000E+00 0.0000000E+00 0.0000000E+00 0.4000000E+02
9 3 2 -0.3500000E+00 0.5723737E+00 0.3224989E+00 0.3904398E+02
10 4 2 -0.3500000E+00 0.1052832E+00 -0.8962571E+00 0.5927114E+02
11 4 1 0.7000000E+00 0.0000000E+00 0.0000000E+00 0.6000000E+02
12 4 2 -0.3500000E+00 -0.1052832E+00 0.8962571E+00 0.6072886E+02
13 5 2 -0.3500000E+00 0.8713731E+00 0.4858468E+00 0.8059183E+02
14 5 1 0.7000000E+00 0.0000000E+00 0.0000000E+00 0.8000000E+02
15 5 2 -0.3500000E+00 -0.8713731E+00 -0.4858468E+00 0.7940817E+02
16 6 2 -0.3500000E+00 0.3094261E+00 0.1893983E+02 0.3548246E+00
17 6 1 0.7000000E+00 0.0000000E+00 0.2000000E+02 0.0000000E+00
18 6 2 -0.3500000E+00 -0.3094261E+00 0.2106017E+02 -0.3548246E+00
19 7 2 -0.3500000E+00 -0.7778275E+00 0.1915416E+02 0.2015854E+02
20 7 1 0.7000000E+00 0.0000000E+00 0.2000000E+02 0.2000000E+02

11
21 7 2 -0.3500000E+00 0.7778275E+00 0.2084584E+02 0.1984146E+02
22 8 2 -0.3500000E+00 0.1129006E+01 0.1996001E+02 0.4026334E+02
23 8 1 0.7000000E+00 0.0000000E+00 0.2000000E+02 0.4000000E+02
24 8 2 -0.3500000E+00 -0.1129006E+01 0.2003999E+02 0.3973666E+02
25 9 2 -0.3500000E+00 -0.1122795E+01 0.2003330E+02 0.5971048E+02
26 9 1 0.7000000E+00 0.0000000E+00 0.2000000E+02 0.6000000E+02
27 9 2 -0.3500000E+00 0.1122795E+01 0.1996670E+02 0.6028952E+02
28 10 2 -0.3500000E+00 -0.8863783E-01 0.2098327E+02 0.8060903E+02
29 10 1 0.7000000E+00 0.0000000E+00 0.2000000E+02 0.8000000E+02
30 10 2 -0.3500000E+00 0.8863783E-01 0.1901673E+02 0.7939097E+02
31 11 2 -0.3500000E+00 -0.3438975E+00 0.4110784E+02 0.4872613E-02
32 11 1 0.7000000E+00 0.0000000E+00 0.4000000E+02 0.0000000E+00
33 11 2 -0.3500000E+00 0.3438975E+00 0.3889216E+02 -0.4872613E-02
34 12 2 -0.3500000E+00 -0.8417580E-02 0.4056014E+02 0.2101576E+02
35 12 1 0.7000000E+00 0.0000000E+00 0.4000000E+02 0.2000000E+02
36 12 2 -0.3500000E+00 0.8417580E-02 0.3943986E+02 0.1898424E+02
37 13 2 -0.3500000E+00 -0.5598126E+00 0.3902219E+02 0.4027586E+02
38 13 1 0.7000000E+00 0.0000000E+00 0.4000000E+02 0.4000000E+02
39 13 2 -0.3500000E+00 0.5598126E+00 0.4097781E+02 0.3972414E+02
40 14 2 -0.3500000E+00 -0.4539178E+00 0.4106725E+02 0.5997695E+02
41 14 1 0.7000000E+00 0.0000000E+00 0.4000000E+02 0.6000000E+02
42 14 2 -0.3500000E+00 0.4539178E+00 0.3893275E+02 0.6002305E+02
43 15 2 -0.3500000E+00 0.6971430E+00 0.3907605E+02 0.7992312E+02
44 15 1 0.7000000E+00 0.0000000E+00 0.4000000E+02 0.8000000E+02
45 15 2 -0.3500000E+00 -0.6971430E+00 0.4092395E+02 0.8007688E+02
46 16 2 -0.3500000E+00 -0.9341715E+00 0.6057392E+02 0.3788656E+00
47 16 1 0.7000000E+00 0.0000000E+00 0.6000000E+02 0.0000000E+00
48 16 2 -0.3500000E+00 0.9341715E+00 0.5942608E+02 -0.3788656E+00
49 17 2 -0.3500000E+00 0.1067008E+01 0.5985920E+02 0.2043275E+02
50 17 1 0.7000000E+00 0.0000000E+00 0.6000000E+02 0.2000000E+02
51 17 2 -0.3500000E+00 -0.1067008E+01 0.6014080E+02 0.1956725E+02
52 18 2 -0.3500000E+00 0.6086209E+00 0.6017452E+02 0.4097197E+02
53 18 1 0.7000000E+00 0.0000000E+00 0.6000000E+02 0.4000000E+02
54 18 2 -0.3500000E+00 -0.6086209E+00 0.5982548E+02 0.3902803E+02
55 19 2 -0.3500000E+00 0.4150895E+00 0.6001716E+02 0.6108305E+02
56 19 1 0.7000000E+00 0.0000000E+00 0.6000000E+02 0.6000000E+02
57 19 2 -0.3500000E+00 -0.4150895E+00 0.5998284E+02 0.5891695E+02
58 20 2 -0.3500000E+00 -0.1127984E+01 0.5993139E+02 0.7973819E+02
59 20 1 0.7000000E+00 0.0000000E+00 0.6000000E+02 0.8000000E+02
60 20 2 -0.3500000E+00 0.1127984E+01 0.6006861E+02 0.8026181E+02
61 21 2 -0.3500000E+00 0.6711348E+00 0.7905423E+02 -0.2645362E-01
62 21 1 0.7000000E+00 0.0000000E+00 0.8000000E+02 0.0000000E+00
63 21 2 -0.3500000E+00 -0.6711348E+00 0.8094577E+02 0.2645362E-01
64 22 2 -0.3500000E+00 -0.1776712E+00 0.7885480E+02 0.1994946E+02
65 22 1 0.7000000E+00 0.0000000E+00 0.8000000E+02 0.2000000E+02

12
66 22 2 -0.3500000E+00 0.1776712E+00 0.8114520E+02 0.2005054E+02
67 23 2 -0.3500000E+00 0.3536869E+00 0.8094811E+02 0.4056709E+02
68 23 1 0.7000000E+00 0.0000000E+00 0.8000000E+02 0.4000000E+02
69 23 2 -0.3500000E+00 -0.3536869E+00 0.7905189E+02 0.3943291E+02
70 24 2 -0.3500000E+00 0.6191410E+00 0.8098012E+02 0.6004037E+02
71 24 1 0.7000000E+00 0.0000000E+00 0.8000000E+02 0.6000000E+02
72 24 2 -0.3500000E+00 -0.6191410E+00 0.7901988E+02 0.5995963E+02
73 25 2 -0.3500000E+00 0.6112207E+00 0.7994683E+02 0.8098447E+02
74 25 1 0.7000000E+00 0.0000000E+00 0.8000000E+02 0.8000000E+02
75 25 2 -0.3500000E+00 -0.6112207E+00 0.8005317E+02 0.7901553E+02
76 26 2 -0.3500000E+00 0.2076414E+02 0.8103951E+00 -0.3239712E+00
77 26 1 0.7000000E+00 0.2000000E+02 0.0000000E+00 0.0000000E+00
78 26 2 -0.3500000E+00 0.1923586E+02 -0.8103951E+00 0.3239712E+00
79 27 2 -0.3500000E+00 0.2113885E+02 -0.1644978E+00 0.2014687E+02
80 27 1 0.7000000E+00 0.2000000E+02 0.0000000E+00 0.2000000E+02
81 27 2 -0.3500000E+00 0.1886115E+02 0.1644978E+00 0.1985313E+02
82 28 2 -0.3500000E+00 0.2085459E+02 -0.2912865E+00 0.3927170E+02
83 28 1 0.7000000E+00 0.2000000E+02 0.0000000E+00 0.4000000E+02
84 28 2 -0.3500000E+00 0.1914541E+02 0.2912865E+00 0.4072830E+02
85 29 2 -0.3500000E+00 0.1964239E+02 -0.5481121E+00 0.6095775E+02
86 29 1 0.7000000E+00 0.2000000E+02 0.0000000E+00 0.6000000E+02
87 29 2 -0.3500000E+00 0.2035761E+02 0.5481121E+00 0.5904225E+02
88 30 2 -0.3500000E+00 0.2114226E+02 -0.2020738E+00 0.7999726E+02
89 30 1 0.7000000E+00 0.2000000E+02 0.0000000E+00 0.8000000E+02
90 30 2 -0.3500000E+00 0.1885774E+02 0.2020738E+00 0.8000274E+02
91 31 2 -0.3500000E+00 0.2020277E+02 0.2110196E+02 0.3002772E+00
92 31 1 0.7000000E+00 0.2000000E+02 0.2000000E+02 0.0000000E+00
93 31 2 -0.3500000E+00 0.1979723E+02 0.1889804E+02 -0.3002772E+00
94 32 2 -0.3500000E+00 0.2106855E+02 0.1960819E+02 0.2022426E+02
95 32 1 0.7000000E+00 0.2000000E+02 0.2000000E+02 0.2000000E+02
96 32 2 -0.3500000E+00 0.1893145E+02 0.2039181E+02 0.1977574E+02
97 33 2 -0.3500000E+00 0.1959870E+02 0.1893002E+02 0.4019924E+02
98 33 1 0.7000000E+00 0.2000000E+02 0.2000000E+02 0.4000000E+02
99 33 2 -0.3500000E+00 0.2040130E+02 0.2106998E+02 0.3980076E+02
100 34 2 -0.3500000E+00 0.2097821E+02 0.2062127E+02 0.6005219E+02
101 34 1 0.7000000E+00 0.2000000E+02 0.2000000E+02 0.6000000E+02
102 34 2 -0.3500000E+00 0.1902179E+02 0.1937873E+02 0.5994781E+02
103 35 2 -0.3500000E+00 0.2007904E+02 0.2074070E+02 0.7911078E+02
104 35 1 0.7000000E+00 0.2000000E+02 0.2000000E+02 0.8000000E+02
105 35 2 -0.3500000E+00 0.1992096E+02 0.1925930E+02 0.8088922E+02
106 36 2 -0.3500000E+00 0.1905858E+02 0.3974971E+02 -0.6298214E+00
107 36 1 0.7000000E+00 0.2000000E+02 0.4000000E+02 0.0000000E+00
108 36 2 -0.3500000E+00 0.2094142E+02 0.4025029E+02 0.6298214E+00
109 37 2 -0.3500000E+00 0.2073633E+02 0.4009123E+02 0.1910832E+02
110 37 1 0.7000000E+00 0.2000000E+02 0.4000000E+02 0.2000000E+02

13
111 37 2 -0.3500000E+00 0.1926367E+02 0.3990877E+02 0.2089168E+02
112 38 2 -0.3500000E+00 0.1961909E+02 0.4027247E+02 0.3893874E+02
113 38 1 0.7000000E+00 0.2000000E+02 0.4000000E+02 0.4000000E+02
114 38 2 -0.3500000E+00 0.2038091E+02 0.3972753E+02 0.4106126E+02
115 39 2 -0.3500000E+00 0.1915000E+02 0.4068863E+02 0.5961414E+02
116 39 1 0.7000000E+00 0.2000000E+02 0.4000000E+02 0.6000000E+02
117 39 2 -0.3500000E+00 0.2085000E+02 0.3931137E+02 0.6038586E+02
118 40 2 -0.3500000E+00 0.1904555E+02 0.3941541E+02 0.8030476E+02
119 40 1 0.7000000E+00 0.2000000E+02 0.4000000E+02 0.8000000E+02
120 40 2 -0.3500000E+00 0.2095445E+02 0.4058459E+02 0.7969524E+02
121 41 2 -0.3500000E+00 0.2061676E+02 0.5905346E+02 0.2631995E+00
122 41 1 0.7000000E+00 0.2000000E+02 0.6000000E+02 0.0000000E+00
123 41 2 -0.3500000E+00 0.1938324E+02 0.6094654E+02 -0.2631995E+00
124 42 2 -0.3500000E+00 0.2090459E+02 0.5973587E+02 0.2067642E+02
125 42 1 0.7000000E+00 0.2000000E+02 0.6000000E+02 0.2000000E+02
126 42 2 -0.3500000E+00 0.1909541E+02 0.6026413E+02 0.1932358E+02
127 43 2 -0.3500000E+00 0.1904642E+02 0.6021538E+02 0.3937559E+02
128 43 1 0.7000000E+00 0.2000000E+02 0.6000000E+02 0.4000000E+02
129 43 2 -0.3500000E+00 0.2095358E+02 0.5978462E+02 0.4062441E+02
130 44 2 -0.3500000E+00 0.2028985E+02 0.5935720E+02 0.5907892E+02
131 44 1 0.7000000E+00 0.2000000E+02 0.6000000E+02 0.6000000E+02
132 44 2 -0.3500000E+00 0.1971015E+02 0.6064280E+02 0.6092108E+02
133 45 2 -0.3500000E+00 0.1940818E+02 0.5939294E+02 0.8079173E+02
134 45 1 0.7000000E+00 0.2000000E+02 0.6000000E+02 0.8000000E+02
135 45 2 -0.3500000E+00 0.2059182E+02 0.6060706E+02 0.7920827E+02
136 46 2 -0.3500000E+00 0.1979142E+02 0.7888740E+02 -0.2534143E+00
137 46 1 0.7000000E+00 0.2000000E+02 0.8000000E+02 0.0000000E+00
138 46 2 -0.3500000E+00 0.2020858E+02 0.8111260E+02 0.2534143E+00
139 47 2 -0.3500000E+00 0.1965620E+02 0.8106056E+02 0.1967968E+02
140 47 1 0.7000000E+00 0.2000000E+02 0.8000000E+02 0.2000000E+02
141 47 2 -0.3500000E+00 0.2034380E+02 0.7893944E+02 0.2032032E+02
142 48 2 -0.3500000E+00 0.1973549E+02 0.7933783E+02 0.4091497E+02
143 48 1 0.7000000E+00 0.2000000E+02 0.8000000E+02 0.4000000E+02
144 48 2 -0.3500000E+00 0.2026451E+02 0.8066217E+02 0.3908503E+02
145 49 2 -0.3500000E+00 0.2103178E+02 0.8038721E+02 0.5963792E+02
146 49 1 0.7000000E+00 0.2000000E+02 0.8000000E+02 0.6000000E+02
147 49 2 -0.3500000E+00 0.1896822E+02 0.7961279E+02 0.6036208E+02
148 50 2 -0.3500000E+00 0.2032827E+02 0.8091767E+02 0.7937094E+02
149 50 1 0.7000000E+00 0.2000000E+02 0.8000000E+02 0.8000000E+02
150 50 2 -0.3500000E+00 0.1967173E+02 0.7908233E+02 0.8062906E+02
151 51 2 -0.3500000E+00 0.4074241E+02 0.7714055E-01 -0.8879620E+00
152 51 1 0.7000000E+00 0.4000000E+02 0.0000000E+00 0.0000000E+00
153 51 2 -0.3500000E+00 0.3925759E+02 -0.7714055E-01 0.8879620E+00
154 52 2 -0.3500000E+00 0.3890641E+02 -0.3610078E+00 0.1986091E+02
155 52 1 0.7000000E+00 0.4000000E+02 0.0000000E+00 0.2000000E+02

14
156 52 2 -0.3500000E+00 0.4109359E+02 0.3610078E+00 0.2013909E+02
157 53 2 -0.3500000E+00 0.3981034E+02 -0.5133891E+00 0.4102277E+02
158 53 1 0.7000000E+00 0.4000000E+02 0.0000000E+00 0.4000000E+02
159 53 2 -0.3500000E+00 0.4018966E+02 0.5133891E+00 0.3897723E+02
160 54 2 -0.3500000E+00 0.3911390E+02 0.1660410E+00 0.6072997E+02
161 54 1 0.7000000E+00 0.4000000E+02 0.0000000E+00 0.6000000E+02
162 54 2 -0.3500000E+00 0.4088610E+02 -0.1660410E+00 0.5927003E+02
163 55 2 -0.3500000E+00 0.3892428E+02 0.4128036E+00 0.8013422E+02
164 55 1 0.7000000E+00 0.4000000E+02 0.0000000E+00 0.8000000E+02
165 55 2 -0.3500000E+00 0.4107572E+02 -0.4128036E+00 0.7986578E+02
166 56 2 -0.3500000E+00 0.3948189E+02 0.2092986E+02 0.4609907E+00
167 56 1 0.7000000E+00 0.4000000E+02 0.2000000E+02 0.0000000E+00
168 56 2 -0.3500000E+00 0.4051811E+02 0.1907014E+02 -0.4609907E+00
169 57 2 -0.3500000E+00 0.3980882E+02 0.1889398E+02 0.1970712E+02
170 57 1 0.7000000E+00 0.4000000E+02 0.2000000E+02 0.2000000E+02
171 57 2 -0.3500000E+00 0.4019118E+02 0.2110602E+02 0.2029288E+02
172 58 2 -0.3500000E+00 0.4012099E+02 0.2115103E+02 0.4007803E+02
173 58 1 0.7000000E+00 0.4000000E+02 0.2000000E+02 0.4000000E+02
174 58 2 -0.3500000E+00 0.3987901E+02 0.1884897E+02 0.3992197E+02
175 59 2 -0.3500000E+00 0.3946110E+02 0.1951442E+02 0.5909479E+02
176 59 1 0.7000000E+00 0.4000000E+02 0.2000000E+02 0.6000000E+02
177 59 2 -0.3500000E+00 0.4053890E+02 0.2048558E+02 0.6090521E+02
178 60 2 -0.3500000E+00 0.3961356E+02 0.2001118E+02 0.7890632E+02
179 60 1 0.7000000E+00 0.4000000E+02 0.2000000E+02 0.8000000E+02
180 60 2 -0.3500000E+00 0.4038644E+02 0.1998882E+02 0.8109368E+02
181 61 2 -0.3500000E+00 0.4104864E+02 0.4039352E+02 -0.3018209E+00
182 61 1 0.7000000E+00 0.4000000E+02 0.4000000E+02 0.0000000E+00
183 61 2 -0.3500000E+00 0.3895136E+02 0.3960648E+02 0.3018209E+00
184 62 2 -0.3500000E+00 0.4066502E+02 0.3930109E+02 0.2064411E+02
185 62 1 0.7000000E+00 0.4000000E+02 0.4000000E+02 0.2000000E+02
186 62 2 -0.3500000E+00 0.3933498E+02 0.4069891E+02 0.1935589E+02
187 63 2 -0.3500000E+00 0.3959651E+02 0.4080243E+02 0.4073410E+02
188 63 1 0.7000000E+00 0.4000000E+02 0.4000000E+02 0.4000000E+02
189 63 2 -0.3500000E+00 0.4040349E+02 0.3919757E+02 0.3926590E+02
190 64 2 -0.3500000E+00 0.4100364E+02 0.3980229E+02 0.6054701E+02
191 64 1 0.7000000E+00 0.4000000E+02 0.4000000E+02 0.6000000E+02
192 64 2 -0.3500000E+00 0.3899636E+02 0.4019771E+02 0.5945299E+02
193 65 2 -0.3500000E+00 0.4060019E+02 0.3981915E+02 0.7902395E+02
194 65 1 0.7000000E+00 0.4000000E+02 0.4000000E+02 0.8000000E+02
195 65 2 -0.3500000E+00 0.3939981E+02 0.4018085E+02 0.8097605E+02
196 66 2 -0.3500000E+00 0.4059209E+02 0.5902646E+02 0.2173894E+00
197 66 1 0.7000000E+00 0.4000000E+02 0.6000000E+02 0.0000000E+00
198 66 2 -0.3500000E+00 0.3940791E+02 0.6097354E+02 -0.2173894E+00
199 67 2 -0.3500000E+00 0.3909385E+02 0.5931855E+02 0.1975482E+02
200 67 1 0.7000000E+00 0.4000000E+02 0.6000000E+02 0.2000000E+02

15
201 67 2 -0.3500000E+00 0.4090615E+02 0.6068145E+02 0.2024518E+02
202 68 2 -0.3500000E+00 0.4111451E+02 0.5969635E+02 0.4010618E+02
203 68 1 0.7000000E+00 0.4000000E+02 0.6000000E+02 0.4000000E+02
204 68 2 -0.3500000E+00 0.3888549E+02 0.6030365E+02 0.3989382E+02
205 69 2 -0.3500000E+00 0.3912348E+02 0.6045222E+02 0.5938943E+02
206 69 1 0.7000000E+00 0.4000000E+02 0.6000000E+02 0.6000000E+02
207 69 2 -0.3500000E+00 0.4087652E+02 0.5954778E+02 0.6061057E+02
208 70 2 -0.3500000E+00 0.4103661E+02 0.5958111E+02 0.7969085E+02
209 70 1 0.7000000E+00 0.4000000E+02 0.6000000E+02 0.8000000E+02
210 70 2 -0.3500000E+00 0.3896339E+02 0.6041889E+02 0.8030915E+02
211 71 2 -0.3500000E+00 0.4026068E+02 0.7985413E+02 -0.1120879E+01
212 71 1 0.7000000E+00 0.4000000E+02 0.8000000E+02 0.0000000E+00
213 71 2 -0.3500000E+00 0.3973932E+02 0.8014587E+02 0.1120879E+01
214 72 2 -0.3500000E+00 0.4032325E+02 0.7930461E+02 0.1912963E+02
215 72 1 0.7000000E+00 0.4000000E+02 0.8000000E+02 0.2000000E+02
216 72 2 -0.3500000E+00 0.3967675E+02 0.8069539E+02 0.2087037E+02
217 73 2 -0.3500000E+00 0.4000564E+02 0.8079578E+02 0.4084398E+02
218 73 1 0.7000000E+00 0.4000000E+02 0.8000000E+02 0.4000000E+02
219 73 2 -0.3500000E+00 0.3999436E+02 0.7920422E+02 0.3915602E+02
220 74 2 -0.3500000E+00 0.4070046E+02 0.8056484E+02 0.5926794E+02
221 74 1 0.7000000E+00 0.4000000E+02 0.8000000E+02 0.6000000E+02
222 74 2 -0.3500000E+00 0.3929954E+02 0.7943516E+02 0.6073206E+02
223 75 2 -0.3500000E+00 0.3960669E+02 0.7906517E+02 0.7943697E+02
224 75 1 0.7000000E+00 0.4000000E+02 0.8000000E+02 0.8000000E+02
225 75 2 -0.3500000E+00 0.4039331E+02 0.8093483E+02 0.8056303E+02
226 76 2 -0.3500000E+00 0.5985168E+02 -0.4140728E-01 -0.1149734E+01
227 76 1 0.7000000E+00 0.6000000E+02 0.0000000E+00 0.0000000E+00
228 76 2 -0.3500000E+00 0.6014832E+02 0.4140728E-01 0.1149734E+01
229 77 2 -0.3500000E+00 0.6004604E+02 -0.1133278E+01 0.2024323E+02
230 77 1 0.7000000E+00 0.6000000E+02 0.0000000E+00 0.2000000E+02
231 77 2 -0.3500000E+00 0.5995396E+02 0.1133278E+01 0.1975677E+02
232 78 2 -0.3500000E+00 0.6010826E+02 -0.3246343E+00 0.4110837E+02
233 78 1 0.7000000E+00 0.6000000E+02 0.0000000E+00 0.4000000E+02
234 78 2 -0.3500000E+00 0.5989174E+02 0.3246343E+00 0.3889163E+02
235 79 2 -0.3500000E+00 0.6072579E+02 0.2755542E+00 0.5913808E+02
236 79 1 0.7000000E+00 0.6000000E+02 0.0000000E+00 0.6000000E+02
237 79 2 -0.3500000E+00 0.5927421E+02 -0.2755542E+00 0.6086192E+02
238 80 2 -0.3500000E+00 0.6084127E+02 -0.6454398E+00 0.8047039E+02
239 80 1 0.7000000E+00 0.6000000E+02 0.0000000E+00 0.8000000E+02
240 80 2 -0.3500000E+00 0.5915873E+02 0.6454398E+00 0.7952961E+02
241 81 2 -0.3500000E+00 0.5887404E+02 0.2021437E+02 0.1784829E+00
242 81 1 0.7000000E+00 0.6000000E+02 0.2000000E+02 0.0000000E+00
243 81 2 -0.3500000E+00 0.6112596E+02 0.1978563E+02 -0.1784829E+00
244 82 2 -0.3500000E+00 0.6076577E+02 0.1947117E+02 0.2069249E+02
245 82 1 0.7000000E+00 0.6000000E+02 0.2000000E+02 0.2000000E+02

16
246 82 2 -0.3500000E+00 0.5923423E+02 0.2052883E+02 0.1930751E+02
247 83 2 -0.3500000E+00 0.5894306E+02 0.2038161E+02 0.4028784E+02
248 83 1 0.7000000E+00 0.6000000E+02 0.2000000E+02 0.4000000E+02
249 83 2 -0.3500000E+00 0.6105694E+02 0.1961839E+02 0.3971216E+02
250 84 2 -0.3500000E+00 0.5967422E+02 0.2020961E+02 0.5890660E+02
251 84 1 0.7000000E+00 0.6000000E+02 0.2000000E+02 0.6000000E+02
252 84 2 -0.3500000E+00 0.6032578E+02 0.1979039E+02 0.6109340E+02
253 85 2 -0.3500000E+00 0.6048184E+02 0.2096769E+02 0.8042073E+02
254 85 1 0.7000000E+00 0.6000000E+02 0.2000000E+02 0.8000000E+02
255 85 2 -0.3500000E+00 0.5951816E+02 0.1903231E+02 0.7957927E+02
256 86 2 -0.3500000E+00 0.5909509E+02 0.3993188E+02 0.7225586E+00
257 86 1 0.7000000E+00 0.6000000E+02 0.4000000E+02 0.0000000E+00
258 86 2 -0.3500000E+00 0.6090491E+02 0.4006812E+02 -0.7225586E+00
259 87 2 -0.3500000E+00 0.5908672E+02 0.3928523E+02 0.2002519E+02
260 87 1 0.7000000E+00 0.6000000E+02 0.4000000E+02 0.2000000E+02
261 87 2 -0.3500000E+00 0.6091328E+02 0.4071477E+02 0.1997481E+02
262 88 2 -0.3500000E+00 0.5907155E+02 0.4013073E+02 0.3931700E+02
263 88 1 0.7000000E+00 0.6000000E+02 0.4000000E+02 0.4000000E+02
264 88 2 -0.3500000E+00 0.6092845E+02 0.3986927E+02 0.4068300E+02
265 89 2 -0.3500000E+00 0.5988173E+02 0.4067959E+02 0.6093261E+02
266 89 1 0.7000000E+00 0.6000000E+02 0.4000000E+02 0.6000000E+02
267 89 2 -0.3500000E+00 0.6011827E+02 0.3932041E+02 0.5906739E+02
268 90 2 -0.3500000E+00 0.6103419E+02 0.4028690E+02 0.8044015E+02
269 90 1 0.7000000E+00 0.6000000E+02 0.4000000E+02 0.8000000E+02
270 90 2 -0.3500000E+00 0.5896581E+02 0.3971310E+02 0.7955985E+02
271 91 2 -0.3500000E+00 0.5963214E+02 0.6107389E+02 -0.2388226E+00
272 91 1 0.7000000E+00 0.6000000E+02 0.6000000E+02 0.0000000E+00
273 91 2 -0.3500000E+00 0.6036786E+02 0.5892611E+02 0.2388226E+00
274 92 2 -0.3500000E+00 0.5971231E+02 0.5928712E+02 0.2086869E+02
275 92 1 0.7000000E+00 0.6000000E+02 0.6000000E+02 0.2000000E+02
276 92 2 -0.3500000E+00 0.6028769E+02 0.6071288E+02 0.1913131E+02
277 93 2 -0.3500000E+00 0.5929571E+02 0.5914337E+02 0.4034022E+02
278 93 1 0.7000000E+00 0.6000000E+02 0.6000000E+02 0.4000000E+02
279 93 2 -0.3500000E+00 0.6070429E+02 0.6085663E+02 0.3965978E+02
280 94 2 -0.3500000E+00 0.6053997E+02 0.6080253E+02 0.5935970E+02
281 94 1 0.7000000E+00 0.6000000E+02 0.6000000E+02 0.6000000E+02
282 94 2 -0.3500000E+00 0.5946003E+02 0.5919747E+02 0.6064030E+02
283 95 2 -0.3500000E+00 0.5886004E+02 0.5998340E+02 0.7978594E+02
284 95 1 0.7000000E+00 0.6000000E+02 0.6000000E+02 0.8000000E+02
285 95 2 -0.3500000E+00 0.6113996E+02 0.6001660E+02 0.8021406E+02
286 96 2 -0.3500000E+00 0.5986267E+02 0.8010015E+02 0.1147480E+01
287 96 1 0.7000000E+00 0.6000000E+02 0.8000000E+02 0.0000000E+00
288 96 2 -0.3500000E+00 0.6013733E+02 0.7989985E+02 -0.1147480E+01
289 97 2 -0.3500000E+00 0.6055878E+02 0.7900192E+02 0.2019289E+02
290 97 1 0.7000000E+00 0.6000000E+02 0.8000000E+02 0.2000000E+02

17
291 97 2 -0.3500000E+00 0.5944122E+02 0.8099808E+02 0.1980711E+02
292 98 2 -0.3500000E+00 0.5965345E+02 0.7890844E+02 0.3981560E+02
293 98 1 0.7000000E+00 0.6000000E+02 0.8000000E+02 0.4000000E+02
294 98 2 -0.3500000E+00 0.6034655E+02 0.8109156E+02 0.4018440E+02
295 99 2 -0.3500000E+00 0.5911329E+02 0.8046163E+02 0.5941158E+02
296 99 1 0.7000000E+00 0.6000000E+02 0.8000000E+02 0.6000000E+02
297 99 2 -0.3500000E+00 0.6088671E+02 0.7953837E+02 0.6058842E+02
298 100 2 -0.3500000E+00 0.5949999E+02 0.7981899E+02 0.7896907E+02
299 100 1 0.7000000E+00 0.6000000E+02 0.8000000E+02 0.8000000E+02
300 100 2 -0.3500000E+00 0.6050001E+02 0.8018101E+02 0.8103093E+02
301 101 2 -0.3500000E+00 0.7951823E+02 0.1046670E+01 -0.1340859E+00
302 101 1 0.7000000E+00 0.8000000E+02 0.0000000E+00 0.0000000E+00
303 101 2 -0.3500000E+00 0.8048177E+02 -0.1046670E+01 0.1340859E+00
304 102 2 -0.3500000E+00 0.8062666E+02 0.9579918E+00 0.2018747E+02
305 102 1 0.7000000E+00 0.8000000E+02 0.0000000E+00 0.2000000E+02
306 102 2 -0.3500000E+00 0.7937334E+02 -0.9579918E+00 0.1981253E+02
307 103 2 -0.3500000E+00 0.8110623E+02 -0.3191631E+00 0.4014140E+02
308 103 1 0.7000000E+00 0.8000000E+02 0.0000000E+00 0.4000000E+02
309 103 2 -0.3500000E+00 0.7889377E+02 0.3191631E+00 0.3985860E+02
310 104 2 -0.3500000E+00 0.7921918E+02 -0.6231624E+00 0.6058956E+02
311 104 1 0.7000000E+00 0.8000000E+02 0.0000000E+00 0.6000000E+02
312 104 2 -0.3500000E+00 0.8078082E+02 0.6231624E+00 0.5941044E+02
313 105 2 -0.3500000E+00 0.7961317E+02 -0.8928735E+00 0.7936854E+02
314 105 1 0.7000000E+00 0.8000000E+02 0.0000000E+00 0.8000000E+02
315 105 2 -0.3500000E+00 0.8038683E+02 0.8928735E+00 0.8063146E+02
316 106 2 -0.3500000E+00 0.8011418E+02 0.2001731E+02 0.1154237E+01
317 106 1 0.7000000E+00 0.8000000E+02 0.2000000E+02 0.0000000E+00
318 106 2 -0.3500000E+00 0.7988582E+02 0.1998269E+02 -0.1154237E+01
319 107 2 -0.3500000E+00 0.7940403E+02 0.2070460E+02 0.1929717E+02
320 107 1 0.7000000E+00 0.8000000E+02 0.2000000E+02 0.2000000E+02
321 107 2 -0.3500000E+00 0.8059597E+02 0.1929540E+02 0.2070283E+02
322 108 2 -0.3500000E+00 0.7943943E+02 0.2098991E+02 0.3977318E+02
323 108 1 0.7000000E+00 0.8000000E+02 0.2000000E+02 0.4000000E+02
324 108 2 -0.3500000E+00 0.8056057E+02 0.1901009E+02 0.4022682E+02
325 109 2 -0.3500000E+00 0.8088798E+02 0.2011742E+02 0.6073709E+02
326 109 1 0.7000000E+00 0.8000000E+02 0.2000000E+02 0.6000000E+02
327 109 2 -0.3500000E+00 0.7911202E+02 0.1988258E+02 0.5926291E+02
328 110 2 -0.3500000E+00 0.8070646E+02 0.2086631E+02 0.8030987E+02
329 110 1 0.7000000E+00 0.8000000E+02 0.2000000E+02 0.8000000E+02
330 110 2 -0.3500000E+00 0.7929354E+02 0.1913369E+02 0.7969013E+02
331 111 2 -0.3500000E+00 0.7922648E+02 0.4082407E+02 0.2611022E+00
332 111 1 0.7000000E+00 0.8000000E+02 0.4000000E+02 0.0000000E+00
333 111 2 -0.3500000E+00 0.8077352E+02 0.3917593E+02 -0.2611022E+00
334 112 2 -0.3500000E+00 0.8066749E+02 0.4088854E+02 0.1966751E+02
335 112 1 0.7000000E+00 0.8000000E+02 0.4000000E+02 0.2000000E+02

18
336 112 2 -0.3500000E+00 0.7933251E+02 0.3911146E+02 0.2033249E+02
337 113 2 -0.3500000E+00 0.8069549E+02 0.3954844E+02 0.3918884E+02
338 113 1 0.7000000E+00 0.8000000E+02 0.4000000E+02 0.4000000E+02
339 113 2 -0.3500000E+00 0.7930451E+02 0.4045156E+02 0.4081116E+02
340 114 2 -0.3500000E+00 0.8007865E+02 0.4112683E+02 0.5973607E+02
341 114 1 0.7000000E+00 0.8000000E+02 0.4000000E+02 0.6000000E+02
342 114 2 -0.3500000E+00 0.7992135E+02 0.3887317E+02 0.6026393E+02
343 115 2 -0.3500000E+00 0.8096299E+02 0.4019568E+02 0.7938358E+02
344 115 1 0.7000000E+00 0.8000000E+02 0.4000000E+02 0.8000000E+02
345 115 2 -0.3500000E+00 0.7903701E+02 0.3980432E+02 0.8061642E+02
346 116 2 -0.3500000E+00 0.7903127E+02 0.5945997E+02 0.3398998E+00
347 116 1 0.7000000E+00 0.8000000E+02 0.6000000E+02 0.0000000E+00
348 116 2 -0.3500000E+00 0.8096873E+02 0.6054003E+02 -0.3398998E+00
349 117 2 -0.3500000E+00 0.8112387E+02 0.5972470E+02 0.2008208E+02
350 117 1 0.7000000E+00 0.8000000E+02 0.6000000E+02 0.2000000E+02
351 117 2 -0.3500000E+00 0.7887613E+02 0.6027530E+02 0.1991792E+02
352 118 2 -0.3500000E+00 0.8015299E+02 0.5889828E+02 0.4032923E+02
353 118 1 0.7000000E+00 0.8000000E+02 0.6000000E+02 0.4000000E+02
354 118 2 -0.3500000E+00 0.7984701E+02 0.6110172E+02 0.3967077E+02
355 119 2 -0.3500000E+00 0.7890693E+02 0.6006545E+02 0.6038278E+02
356 119 1 0.7000000E+00 0.8000000E+02 0.6000000E+02 0.6000000E+02
357 119 2 -0.3500000E+00 0.8109307E+02 0.5993455E+02 0.5961722E+02
358 120 2 -0.3500000E+00 0.7909845E+02 0.5930084E+02 0.7979030E+02
359 120 1 0.7000000E+00 0.8000000E+02 0.6000000E+02 0.8000000E+02
360 120 2 -0.3500000E+00 0.8090155E+02 0.6069916E+02 0.8020970E+02
361 121 2 -0.3500000E+00 0.7905708E+02 0.8067231E+02 -0.6699613E-01
362 121 1 0.7000000E+00 0.8000000E+02 0.8000000E+02 0.0000000E+00
363 121 2 -0.3500000E+00 0.8094292E+02 0.7932769E+02 0.6699613E-01
364 122 2 -0.3500000E+00 0.8072867E+02 0.8034531E+02 0.1916609E+02
365 122 1 0.7000000E+00 0.8000000E+02 0.8000000E+02 0.2000000E+02
366 122 2 -0.3500000E+00 0.7927133E+02 0.7965469E+02 0.2083391E+02
367 123 2 -0.3500000E+00 0.7996616E+02 0.7890097E+02 0.3963043E+02
368 123 1 0.7000000E+00 0.8000000E+02 0.8000000E+02 0.4000000E+02
369 123 2 -0.3500000E+00 0.8003384E+02 0.8109903E+02 0.4036957E+02
370 124 2 -0.3500000E+00 0.7916423E+02 0.8041742E+02 0.6068763E+02
371 124 1 0.7000000E+00 0.8000000E+02 0.8000000E+02 0.6000000E+02
372 124 2 -0.3500000E+00 0.8083577E+02 0.7958258E+02 0.5931237E+02
373 125 2 -0.3500000E+00 0.7897990E+02 0.7955697E+02 0.7967028E+02
374 125 1 0.7000000E+00 0.8000000E+02 0.8000000E+02 0.8000000E+02
375 125 2 -0.3500000E+00 0.8102010E+02 0.8044303E+02 0.8032972E+02
Bonds
1 1 1 2
2 1 2 3

19
3 1 4 5
4 1 5 6
5 1 7 8
6 1 8 9
7 1 10 11
8 1 11 12
9 1 13 14
10 1 14 15
11 1 16 17
12 1 17 18
13 1 19 20
14 1 20 21
15 1 22 23
16 1 23 24
17 1 25 26
18 1 26 27
19 1 28 29
20 1 29 30
21 1 31 32
22 1 32 33
23 1 34 35
24 1 35 36
25 1 37 38
26 1 38 39
27 1 40 41
28 1 41 42
29 1 43 44
30 1 44 45
31 1 46 47
32 1 47 48
33 1 49 50
34 1 50 51
35 1 52 53
36 1 53 54
37 1 55 56
38 1 56 57
39 1 58 59
40 1 59 60
41 1 61 62
42 1 62 63
43 1 64 65
44 1 65 66
45 1 67 68
46 1 68 69
47 1 70 71

20
48 1 71 72
49 1 73 74
50 1 74 75
51 1 76 77
52 1 77 78
53 1 79 80
54 1 80 81
55 1 82 83
56 1 83 84
57 1 85 86
58 1 86 87
59 1 88 89
60 1 89 90
61 1 91 92
62 1 92 93
63 1 94 95
64 1 95 96
65 1 97 98
66 1 98 99
67 1 100 101
68 1 101 102
69 1 103 104
70 1 104 105
71 1 106 107
72 1 107 108
73 1 109 110
74 1 110 111
75 1 112 113
76 1 113 114
77 1 115 116
78 1 116 117
79 1 118 119
80 1 119 120
81 1 121 122
82 1 122 123
83 1 124 125
84 1 125 126
85 1 127 128
86 1 128 129
87 1 130 131
88 1 131 132
89 1 133 134
90 1 134 135
91 1 136 137
92 1 137 138

21
93 1 139 140
94 1 140 141
95 1 142 143
96 1 143 144
97 1 145 146
98 1 146 147
99 1 148 149
100 1 149 150
101 1 151 152
102 1 152 153
103 1 154 155
104 1 155 156
105 1 157 158
106 1 158 159
107 1 160 161
108 1 161 162
109 1 163 164
110 1 164 165
111 1 166 167
112 1 167 168
113 1 169 170
114 1 170 171
115 1 172 173
116 1 173 174
117 1 175 176
118 1 176 177
119 1 178 179
120 1 179 180
121 1 181 182
122 1 182 183
123 1 184 185
124 1 185 186
125 1 187 188
126 1 188 189
127 1 190 191
128 1 191 192
129 1 193 194
130 1 194 195
131 1 196 197
132 1 197 198
133 1 199 200
134 1 200 201
135 1 202 203
136 1 203 204
137 1 205 206

22
138 1 206 207
139 1 208 209
140 1 209 210
141 1 211 212
142 1 212 213
143 1 214 215
144 1 215 216
145 1 217 218
146 1 218 219
147 1 220 221
148 1 221 222
149 1 223 224
150 1 224 225
151 1 226 227
152 1 227 228
153 1 229 230
154 1 230 231
155 1 232 233
156 1 233 234
157 1 235 236
158 1 236 237
159 1 238 239
160 1 239 240
161 1 241 242
162 1 242 243
163 1 244 245
164 1 245 246
165 1 247 248
166 1 248 249
167 1 250 251
168 1 251 252
169 1 253 254
170 1 254 255
171 1 256 257
172 1 257 258
173 1 259 260
174 1 260 261
175 1 262 263
176 1 263 264
177 1 265 266
178 1 266 267
179 1 268 269
180 1 269 270
181 1 271 272
182 1 272 273

23
183 1 274 275
184 1 275 276
185 1 277 278
186 1 278 279
187 1 280 281
188 1 281 282
189 1 283 284
190 1 284 285
191 1 286 287
192 1 287 288
193 1 289 290
194 1 290 291
195 1 292 293
196 1 293 294
197 1 295 296
198 1 296 297
199 1 298 299
200 1 299 300
201 1 301 302
202 1 302 303
203 1 304 305
204 1 305 306
205 1 307 308
206 1 308 309
207 1 310 311
208 1 311 312
209 1 313 314
210 1 314 315
211 1 316 317
212 1 317 318
213 1 319 320
214 1 320 321
215 1 322 323
216 1 323 324
217 1 325 326
218 1 326 327
219 1 328 329
220 1 329 330
221 1 331 332
222 1 332 333
223 1 334 335
224 1 335 336
225 1 337 338
226 1 338 339
227 1 340 341

24
228 1 341 342
229 1 343 344
230 1 344 345
231 1 346 347
232 1 347 348
233 1 349 350
234 1 350 351
235 1 352 353
236 1 353 354
237 1 355 356
238 1 356 357
239 1 358 359
240 1 359 360
241 1 361 362
242 1 362 363
243 1 364 365
244 1 365 366
245 1 367 368
246 1 368 369
247 1 370 371
248 1 371 372
249 1 373 374
250 1 374 375
Angles
1 1 1 2 3
2 1 4 5 6
3 1 7 8 9
4 1 10 11 12
5 1 13 14 15
6 1 16 17 18
7 1 19 20 21
8 1 22 23 24
9 1 25 26 27
10 1 28 29 30
11 1 31 32 33
12 1 34 35 36
13 1 37 38 39
14 1 40 41 42
15 1 43 44 45
16 1 46 47 48
17 1 49 50 51
18 1 52 53 54
19 1 55 56 57

25
20 1 58 59 60
21 1 61 62 63
22 1 64 65 66
23 1 67 68 69
24 1 70 71 72
25 1 73 74 75
26 1 76 77 78
27 1 79 80 81
28 1 82 83 84
29 1 85 86 87
30 1 88 89 90
31 1 91 92 93
32 1 94 95 96
33 1 97 98 99
34 1 100 101 102
35 1 103 104 105
36 1 106 107 108
37 1 109 110 111
38 1 112 113 114
39 1 115 116 117
40 1 118 119 120
41 1 121 122 123
42 1 124 125 126
43 1 127 128 129
44 1 130 131 132
45 1 133 134 135
46 1 136 137 138
47 1 139 140 141
48 1 142 143 144
49 1 145 146 147
50 1 148 149 150
51 1 151 152 153
52 1 154 155 156
53 1 157 158 159
54 1 160 161 162
55 1 163 164 165
56 1 166 167 168
57 1 169 170 171
58 1 172 173 174
59 1 175 176 177
60 1 178 179 180
61 1 181 182 183
62 1 184 185 186
63 1 187 188 189
64 1 190 191 192

26
65 1 193 194 195
66 1 196 197 198
67 1 199 200 201
68 1 202 203 204
69 1 205 206 207
70 1 208 209 210
71 1 211 212 213
72 1 214 215 216
73 1 217 218 219
74 1 220 221 222
75 1 223 224 225
76 1 226 227 228
77 1 229 230 231
78 1 232 233 234
79 1 235 236 237
80 1 238 239 240
81 1 241 242 243
82 1 244 245 246
83 1 247 248 249
84 1 250 251 252
85 1 253 254 255
86 1 256 257 258
87 1 259 260 261
88 1 262 263 264
89 1 265 266 267
90 1 268 269 270
91 1 271 272 273
92 1 274 275 276
93 1 277 278 279
94 1 280 281 282
95 1 283 284 285
96 1 286 287 288
97 1 289 290 291
98 1 292 293 294
99 1 295 296 297
100 1 298 299 300
101 1 301 302 303
102 1 304 305 306
103 1 307 308 309
104 1 310 311 312
105 1 313 314 315
106 1 316 317 318
107 1 319 320 321
108 1 322 323 324
109 1 325 326 327

27
110 1 328 329 330
111 1 331 332 333
112 1 334 335 336
113 1 337 338 339
114 1 340 341 342
115 1 343 344 345
116 1 346 347 348
117 1 349 350 351
118 1 352 353 354
119 1 355 356 357
120 1 358 359 360
121 1 361 362 363
122 1 364 365 366
123 1 367 368 369
124 1 370 371 372
125 1 373 374 375

fix_rigid_example.pdf

More Related Content

Similar to fix_rigid_example.pdf (20)

Recently uploaded (20)

fix_rigid_example.pdf