Hamiltonian Method: Getting Final Equation of Motion

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SUMMARY

The Hamiltonian method for deriving the final equation of motion involves starting with the Lagrangian, defined as the difference between kinetic energy (T) and potential energy (U). The process includes calculating momentum using the formula ∂L/∂q̇, transitioning to the Hamiltonian by summing T and U, and applying Hamilton's equations of motion. The confusion arises when determining the time derivatives at the end of the process, which are essential for obtaining the final equations of motion. For clarity, refer to the provided Harvard resource for detailed examples.

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  • Understanding of Lagrangian mechanics
  • Familiarity with Hamiltonian mechanics
  • Knowledge of kinetic and potential energy concepts
  • Ability to compute partial derivatives
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  • Explore examples of deriving equations of motion using the Hamiltonian method
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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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