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Consider the Atwood machine of Figure 13.2, but suppose

Chapter 13, Problem 13.3

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QUESTION:

Consider the Atwood machine of figure 13.2, but suppose that the pulley is a uniform disc of mass  and radius . Using  as your generalized coordinate, write down the lagrangian, the generalised momentum  and the Hamitonian . Find Hamilton’s equations and use them to find the acceleration  .

                                               

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QUESTION:

Consider the Atwood machine of figure 13.2, but suppose that the pulley is a uniform disc of mass  and radius . Using  as your generalized coordinate, write down the lagrangian, the generalised momentum  and the Hamitonian . Find Hamilton’s equations and use them to find the acceleration  .

                                               

ANSWER:

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Langrangian and Hamiltonian are two different methods which are used for the evaluation and understanding of classical physics.

Mathematically the Hamiltonian equation for particle or object is expressed as;

                                                                           

Here  is the derivative of the position of the particle,  ,  is the Lagrangian and  is the Hamiltonian.

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