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A one-degree-of-freedom mechanical system is described by the foIlowing Lagrangian: L(Q, Q, t) = cos² øt 2 - QQ sin 2ot – cos 2wt . 2 (a) Find the corresponding Hamiltonian. (b) Is this Hamiltonian a constant of the motion? (c) Show that the Hamiltonian expressed in terms of the new variable q = Q cos wt and its conjugate momentum does not explicitly depend on time. What physical system does it describe?

A one-degree-of-freedom mechanical system is described by the foIlowing Lagrangian: L(Q, Q, t) = cos² øt 2 - QQ sin 2ot – cos 2wt . 2 (a) Find the corresponding Hamiltonian. (b) Is this Hamiltonian a constant of the motion? (c) Show that the Hamiltonian expressed in terms of the new variable q = Q cos wt and its conjugate momentum does not explicitly depend on time. What physical system does it describe?

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7.5 A one-degree-of-freedom mechanical system is described by the following Lagrangian: LQ, Q, 1) = cos² wt 2 - 00 sin 201 – QQ sin 2ot cos 2wt. 2 (a) Find the corresponding Hamiltonian. (b) Is this Hamiltonian a constant of the motion? (c) Show that the Hamiltonian expressed in terms of the new variable q = Q cos wt and its conjugate momentum does not explicitly depend on time. What physical system does it describe? %3D
Transcribed Image Text:7.5 A one-degree-of-freedom mechanical system is described by the following Lagrangian: LQ, Q, 1) = cos² wt 2 - 00 sin 201 – QQ sin 2ot cos 2wt. 2 (a) Find the corresponding Hamiltonian. (b) Is this Hamiltonian a constant of the motion? (c) Show that the Hamiltonian expressed in terms of the new variable q = Q cos wt and its conjugate momentum does not explicitly depend on time. What physical system does it describe? %3D
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