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# Lagrangian and Hamiltonian dynamics of a particle

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A particle of mass m moves in one dimension under the influence of a force:

F(x, t) = (k/x^2)*e^(-t/T)

Where k and T are positive constants.

a) Compute the Lagrangian and Hamiltonian Functions

b) Compare the Hamiltonian and the total energy.

c) Discuss the conservation of energy for the system.

https://brainmass.com/physics/conservation-of-energy/lagrangian-hamiltonian-dynamics-particle-99716

#### Solution Preview

Please see the attached file for detailed solution.

A particle of mass m moves in one demension under the influence of a force:

F(x, t) = (k/x^2)*e^(-t/T)

Where k and T are positive constants.

a) Compute ...

#### Solution Summary

The solution is a detailed explanation on Lagrangian and Hamiltonian dynamics of a particle which moves in one dimension under the influence of a force. The Lagrangian and Hamiltonian functions of the particle are calculated. Furthermore, the conservation of energy of the system is discussed.

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