Newton, Lagrange, Hamilton and Hamilton-Jacobi Mechanics of Classical Particles with Mathematica.nb
Newton, Lagrange, Hamilton and HamiltonJacobi Mechanics of Classical Particles with Mathematica Dr. Luigi E. Masciovecchio email:
[email protected] First published and available as notebook and PDF on http://sites.google.com/site/luigimasciovecchio/ 2017.06.06 In[1]:=
Print@"Document revision: ", IntegerPart@Date@DDD Document revision: 82017, 10, 17, 6, 57, 57
0D - k x@tD - m x¢¢ @tD 0
Out[229]=
Out[231]=
99x@tD ® a CosA
I- 1 + b12 M Ha - xL2
k tE== m
In[232]:=
FirstIntegrals@L, x@tD, tD
2 Ha - xL
=
=
34
Newton, Lagrange, Hamilton and Hamilton-Jacobi Mechanics of Classical Particles with Mathematica.nb
Out[232]=
9FirstIntegral@tD ®
1 2
Ik x@tD2 + m x¢ @tD2 M=
2D nonlinear pendulum In[233]:=
Remove@"Global`*"D T = m 2 Ix¢ @tD2 + y¢ @tD2 M;
In[234]:=
V = m g y@tD; L = T-V Out[236]=
- g m y@tD +
1 2
m Ix¢ @tD2 + y¢ @tD2 M
8x ® H- l Sin@Θ@ð DD &L, y ® H- l Cos@Θ@ð DD &L 0 && m > 0D
In[237]:=
Out[238]=
g l m Cos@Θ@tDD +
1 2
m Il2 Cos@Θ@tDD2 Θ¢ @tD2 + l2 Sin@Θ@tDD2 Θ¢ @tD2 M
Out[239]=
9FirstIntegral@tD ®
1 2
l m I- 2 g Cos@Θ@tDD + l Θ¢ @tD2 M=
g Sin@Θ@tDD + l Θ¢¢ @tD 0
Out[241]=
In[242]:=
Print@"Linearization..."D %% . Sin ® HSeries@Sin@ð D, 8ð , 0, 1
