By Sidney B. Cahn, Boris E. Nadgorny, C.N. Yang
With a view to arm hopeful graduate scholars with the information essential to move the qualifying exam, the authors have assembled and solved typical and unique difficulties from 4 significant American universities and Moscow Phys-Tech. quite a lot of fabric is roofed and comparisons are made among comparable difficulties of various colleges to supply the scholar with sufficient details to consider cozy and assured on the examination.
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Additional resources for A Guide to Physics Problems: Mechanics, Relativity, and Electrodynamics
31 MECHANICS a) Write the Lagrangian and the Hamiltonian, and rewrite them in terms of the variables b) Find an integral of motion other than the energy, and show that its Poisson bracket with is zero. 51 Particle in Magnetic Field (Stony Brook) a) Give a relationship between Hamilton’s equations under a canonical transformation. Verify that the transformation is canonical. 52 introduced above, using Adiabatic Invariants (Boston (a)) and Dissolving Spring (Princeton, MIT (b)) a) (Adiabatic Invariants) Consider a system with canonical variables At the time and let be an arbitrary closed path in phase space 32 PROBLEMS Assume that the point moves in phase space according to of Hamilton's equations.
47). a) Find an expression for the velocity of the water b) Find the corresponding dispersion relation. You may assume that the flow of the water is irrotational that the amplitude of the waves is small (in practice, this means that where is the MECHANICS 29 height of the waves), that surface tension effects are not important, and that water is incompressible. 48 Suspension Bridge (Stony Brook) A flexible massless cable in a suspension bridge is subject to uniform loading along the The weight of the load per unit length of the cable is and the tension in the cable at the center of the bridge (at is (see Figure P.
What is the force law? 17 11 Dumbbell Satellite (Maryland, MIT, Michigan State) Automatic stabilization of the orientation of orbiting satellites utilizes the torque from the Earth’s gravitational pull on a non-spherical satellite in a circular orbit of radius R. 17). The orientation of the satellite relative to the direction toward the Earth is measured by angle a) Determine the value of for the stable orientation of the satellite. b) Show that the angular frequency of small-angle oscillations of the satellite about its stable orientation is times the orbital angular velocity of the satellite.
A Guide to Physics Problems: Mechanics, Relativity, and Electrodynamics by Sidney B. Cahn, Boris E. Nadgorny, C.N. Yang