A particle of mass m is acted on by a force whose potential energy is U...

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A particle of mass m is acted on by a force whose potential energy is U (r). (a) Obtain the Lagrangian function in a spherical coordinate system which is rotating with constant angular speed 2 about the z-axis. (b) Show that your Lagrangian function has the same form as in a fixed coordinate system with the addition of a velocity-dependent potential energy function U' which gives the centrifugal and Coriolis forces. (c) Calculate from the velocity-dependent potential U' the components of the centrifugal and Coriolis forces in the radial and azimuthal directions. A particle of mass m is acted on by a force whose potential energy is U (r). (a) Obtain the Lagrangian function in a spherical coordinate system which is rotating with constant angular speed 2 about the z-axis. (b) Show that your Lagrangian function has the same form as in a fixed coordinate system with the addition of a velocity-dependent potential energy function U' which gives the centrifugal and Coriolis forces. (c) Calculate from the velocity-dependent potential U' the components of the centrifugal and Coriolis forces in the radial and azimuthal directions.