Hamiltonian Method: Getting Final Equation of Motion

In summary, the conversation was about the procedure for finding the equation of motion using the Lagrangian and Hamiltonian equations. The person was confused about taking time derivatives at the end of some examples. A helpful resource was suggested for further understanding.
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oldspice1212
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Hey, I was hoping someone could clear this up for me. When using this method, how do you get the final equation of motion, that's where I am confused.

So I know I start off using Lagrangian (T - U) -> momentum (partial L/ partial q dot) -> Hamiltonian T+U, and then using the hamiltonian equation's of motion, we find the equations ( I can do this part). This is just a quick summary of the procedure. But, for some examples, they are taking time derivatives at the end for some equations, and finding the equation of motion. I don't understand why and where they come from?
Could someone please explain, thanks.
 
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1. What is the Hamiltonian method?

The Hamiltonian method is a mathematical tool used to describe the dynamics of a system in terms of its position and momentum variables. It is commonly used in physics and engineering to determine the equations of motion for a system.

2. How does the Hamiltonian method differ from other methods of determining equations of motion?

The Hamiltonian method differs from other methods, such as the Lagrangian method, in that it takes into account both the position and momentum variables of a system. It also allows for the inclusion of external forces and constraints in the equations of motion.

3. What is the final equation of motion obtained using the Hamiltonian method?

The final equation of motion obtained using the Hamiltonian method is known as the Hamilton's equations. These equations describe the time evolution of a system's position and momentum variables, and can be used to predict the future behavior of the system.

4. How is the Hamiltonian method used in practical applications?

The Hamiltonian method is used in a variety of practical applications, including classical mechanics, quantum mechanics, and control theory. It is particularly useful for studying the dynamics of complex systems, such as celestial bodies or quantum particles.

5. Are there any limitations to the Hamiltonian method?

While the Hamiltonian method is a powerful tool for determining equations of motion, it does have some limitations. It is only applicable to systems that can be described by a set of position and momentum variables, and it does not take into account the effects of friction or other dissipative forces.

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