Aparticle of mass m is constrained to move on the inside surface of a smooth cone of half-angle α (see figure 7-2). the particle is subject to a gravitational force. determine a set of generalized coordinates and determine the con- straints. find lagrange's equations of motion, equation 7.18. solution. let the axis of the cone correspond to the z-axis and let the apex of the cone be located at the origin. since the problem possesses cylindrical sym- metry, we choose , θ, and z as the generalized coordinates, we have, however, the equation of constraint (7.26) 241 7.4 lagrange's equations of motion in generalized coordinates