Consider a particle of mass m constrained to move on the surface of a cone of half-angle a as shown in the figure below. (a) Write down all constraint relations in cylindrical coordinates. (b) Show that the number s of degrees of freedom is eaual 2. (c) Choose s convenient generalized coordinates. (d) Obtain expressions for the kinetic energy, potential energy. and Lagrangian function in spherical generalized coordinates. (e) Determine if any coordinate(s) are ignorable (f) Obtain expressions for the generalized momenta, m (g) Write down the Lagrange equations of motion.

Consider a particle of mass m constrained to move on the surface of a cone of half-angle a as shown in the figure below. (a) Write down all constraint relations in cylindrical coordinates. (b) Show that the number s of degrees of freedom is eaual 2. (c) Choose s convenient generalized coordinates. (d) Obtain expressions for the kinetic energy, potential energy. and Lagrangian function in spherical generalized coordinates. (e) Determine if any coordinate(s) are ignorable (f) Obtain expressions for the generalized momenta, m (g) Write down the Lagrange equations of motion.