Classical Mechanics-Lagrangian and Hamiltonian Formalism and Equations of Motion (CSIR Physical Sciences): Questions 11 - 12 of 12

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Question number: 11

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

Appeared in Year: 2011

MCQ▾

Question

The Hamiltonian of a particle of unit mass moving in the XY – plane is given to be:

H=xPxyPy12x2+12y2 in suitable units. The initial values are given to be (x(0),y(0))=(1, 1) and (Px(0),Py(0))=(12,12) . During the motion, the curves traced out by the particles in the xy – plane and the PxPy plane are (June)

Choices

Choice (4) Response

a.

both hyperbolas

b.

both straight lines

c.

a hyperbola and an ellipse, respectively

d.

a straight line and a hyperbola respectively

Question number: 12

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

Appeared in Year: 2016

MCQ▾

Question

The Hamiltonian of a system with generalized coordinate and momentum (q,p) is H=p2q2 . A solution of the Hamiltonian equation of motion is – (in the following A and B are constants) (June)

Choices

Choice (4) Response

a.

p=Be2At,q=ABe2At

b.

p=AeAt,q=ABeAt

c.

p=Ae2At,q=ABe2At

d.

p=2AeA2t,q=ABeA2t

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