How Do You Write a Hamiltonian Function for Specific Dynamical Systems?

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The discussion revolves around writing the Hamiltonian function for two specific dynamical systems involving a constant A and a function u of time. The first system is described by the equation u'' + u = A(1 + 2u + 3u^2), while the second is u'' + u = A/((1 - u)^2). A suggestion is made to use Lagrange's equations to derive the Lagrangian and subsequently the Hamiltonian. The original poster expresses difficulty in solving these systems and references a related thread for further assistance. The conversation highlights the complexities of nonlinear dynamical systems and the methods to approach their solutions.
dekarman
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Hi,

I need some help in writing the Hamiltonian function for the following dynamical systems.

1) u''+u=A (1+2*u+3*u^2)

2) u''+u=A/((1-u)^2);

In both cases A is a constant and u is a function of t.

Any help would be greatly appreciated.

Thank you.

Manish
 
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You can write out Lagrange's equations and integrate in order to solve for the Lagrangian. Then proceed in the usual manner to get the Hamiltonian.
 
Hi Thanks Dalespam,

Actually, I am facing trouble in solving certain dynamical system. You can refer to my new thread titled "Discrepancy in the solution of a nonlinear dynamical system".
 

Thread 'Reference frames, center of rotation, etc'

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