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

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SUMMARY

This discussion focuses on writing Hamiltonian functions for specific dynamical systems represented by the equations u'' + u = A(1 + 2u + 3u^2) and u'' + u = A/((1-u)^2). The user, Manish, seeks assistance in deriving the Hamiltonian from these equations. Dalespam suggests using Lagrange's equations and integrating to find the Lagrangian, which is a standard approach to subsequently derive the Hamiltonian. This method is essential for analyzing the dynamics of the given systems.

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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".
 

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