Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Particle of mass m slides without friction on a wedge of angle alpha and mass M that can move without friction on a smooth horizontal surface,as shown in the figure.Treating the constraint of the particle on the wedge by the method of Lagrange multipliers,find the equation of motion for the particle and wedge.Also obtain an expression for the forces of constraint.Calculate the work done in time t by the forces of constraint acting on the particle and on the wedge.what are the constants of motion for the
(a) The Hamiltonian for a system has the formH = 1/2 (1/q2+ p2q4)..Find the equation of motion for q.
(b) Find a canonical transformation that reduces H to the form of harmonic oscillator. Show that the solution for the transformed variables is suchthat the equation of motion found in part (a) is satisfied.
Verify that the Hamiltonian equationH(x, p, t) = T + V = p2/2m + (k/2) (x − v0t)2leads to the same motion as described by the following equation:mx¨'= −kx', where x' = x − v0t.
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