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Physics, 02.09.2019 19:30 audrey435

Lagrangian mechanics. determine the equations of motion for a particle of mass m constrained to move on the surface of a cone in the presence of gravity. the cone has half-angle 45° and is oriented vertically, so that (using cylindrical coordinates) r-z with θ unconstrained. the gravitational potential is mg. thus there are two equations of motion, one for z (or, equivalently, for r) and one for θ. you do not need to solve the equations of motion. however, you should give an expression for one conserved quantity other than the total energy, and state its physical interpretation. (a conserved quantity is one that does not depend on time).

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