Help needed in writing the Hamiltonian function

In summary, the conversation is about needing help in writing the Hamiltonian function for two different dynamical systems with a constant and a function of t. The suggestion is to use Lagrange's equations and integrate to solve for the Lagrangian, and then proceed to get the Hamiltonian. The person also mentions facing trouble in solving a particular dynamical system and asks for help in a new thread.
  • #1
dekarman
7
0
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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  • #2
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.
 
  • #3
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".
 

1. What is a Hamiltonian function?

A Hamiltonian function, also known as the Hamiltonian, is a mathematical function that describes the total energy of a physical system. It is commonly used in classical mechanics and quantum mechanics to study the dynamics of a system over time.

2. Why is the Hamiltonian function important?

The Hamiltonian function is important because it allows us to model the behavior of a physical system and make predictions about its future states. It is also a fundamental concept in symplectic geometry and has applications in many areas of physics and engineering.

3. How is the Hamiltonian function written?

The Hamiltonian function is typically written as H = T + V, where T represents the kinetic energy of the system and V represents the potential energy. In quantum mechanics, it is often written using operators and the Schrödinger equation.

4. What are the key components of the Hamiltonian function?

The key components of the Hamiltonian function are the position and momentum variables of the system, as well as the potential energy function. In quantum mechanics, it also includes the wave function and the Hamiltonian operator.

5. How can I use the Hamiltonian function in my research?

The Hamiltonian function can be used in a variety of research fields, including physics, engineering, and mathematics. It can help you analyze the behavior of a system and make predictions about its future states. Additionally, it can be used to develop new models and theories in your field of study.

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