In Example 3.8, find Q1 and Q2 in terms of the components of F by considering the work done under suitable small displacements. Check that the same expressions for the Qas follow from the chain rule in the case that F = -?U. A particle of mass m is subject to a force F. Obtain the equations of motion in cylindrical polar coordinates. A particle of unit mass is subject to an inverse-square-law central force where r = |r| and r is the position vector from the origin of an inertial frame. Show that the motion is governed by the Lagrangian Write down the equations of motion in spherical polar

In Example 3.8, find Q1 and Q2 in terms of the components of F by considering the work done under suitable small displacements. Check that the same expressions for the Qas follow from the chain rule in the case that F = -?U. A particle of mass m is subject to a force F. Obtain the equations of motion in cylindrical polar coordinates. A particle of unit mass is subject to an inverse-square-law central force where r = |r| and r is the position vector from the origin of an inertial frame. Show that the motion is governed by the Lagrangian Write down the equations of motion in spherical polar coordinates and show that there are solutions with ? = p/2 throughout the motion.

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