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DEtools[hamilton_eqs] - generate Hamilton equations

Calling Sequence

hamilton_eqs(H)

Parameters

H

-

any algebraic expression representing the Hamiltonian

Description

• 

hamilton_eqs receives a Hamiltonian and returns a sequence with Hamilton's equations and a list with the p's and q's involved.

• 

Some useful conventions were adopted to represent the p's and q's. All p's and q's must appear as pn or qn where n is a positive integer, as in p1, p2, and the time dependence need not be explicit, as in pn or qn instead of pn(t) or qn(t). The Hamilton equations will be automatically returned using pn(t) or qn(t).

• 

This function is part of the DEtools package, and so it can be used in the form hamilton_eqs(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[hamilton_eqs](..).

Examples

withDEtools:

The Toda Hamiltonian

H:=1p12+p222+1ⅇ2q2+23q1+ⅇ2q223q1+ⅇ4q22418

H:=12p12+12p22+124ⅇ2q2+23q1+124ⅇ2q223q1+124ⅇ4q218

(1)

hamilton_eqsH

ⅆⅆtp1t=1123ⅇ2q2t+23q1t+1123ⅇ2q2t23q1t,ⅆⅆtp2t=112ⅇ2q2t+23q1t112ⅇ2q2t23q1t+16ⅇ4q2t,ⅆⅆtq1t=p1t,ⅆⅆtq2t=p2t,p1t,p2t,q1t,q2t

(2)

The Henon-Heiles Hamiltonian

H:=1p12+p22+q12+q222+q12q2q233

H:=12p12+12p22+12q12+12q22+q12q213q23

(3)

hamilton_eqsH

ⅆⅆtp1t=2q1tq2tq1t,ⅆⅆtp2t=q1t2+q2t2q2t,ⅆⅆtq1t=p1t,ⅆⅆtq2t=p2t,p1t,p2t,q1t,q2t

(4)

See Also

DEtools, generate_ic, PDEtools, poincare, Poincare


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