m 1. (15 points) Consider two masses mi and m2 that are free to move on a circular frictionless wire of radius R. The ma
Posted: Sat Feb 26, 2022 11:50 am
- M 1 15 Points Consider Two Masses Mi And M2 That Are Free To Move On A Circular Frictionless Wire Of Radius R The Ma 1 (67.96 KiB) Viewed 35 times
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Part a) asks for the Lagrangian: L = KE - PE
(θ1 in this case is the angle from the origin(center) of the
loop to mass 1, and θ2 is the angle from the origin of the
loop to mass 2.)
m 1. (15 points) Consider two masses mi and m2 that are free to move on a circular frictionless wire of radius R. The masses are kept a linear distance l < R apart by a massless rod. The masses move under the influence of gravity and the normal force of the wire. 81 m2 (a) Find the Lagrangian for the system, using the angular position 0 of one of the masses to parameterize the position of the masses. (b) Find the equations of motion for 0. (c) Find an equation for the equilibrium position (eg of the system. The equation does not have a simple analytic solution. Find the solution for the case mı = m2, and explain the qualitative behavior of the solution as a function of the ratio mı/m2. (d) Find the linearized equations of motion for small deviations about the equilibrium. Leave your result in terms of (eq. Is the equilibrium stable or unstable? Give a physical argument, as well as a mathematical argument based on the equations. Extra credit: (10 points) Find the equations of motion of this system using Newton's laws.