α: g tos 2 h I. A cone of height h and cone-angle a has moments of inertia 11 = 12 and 13. We denote the body-frame coor

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α: g tos 2 h I. A cone of height h and cone-angle a has moments of inertia 11 = 12 and 13. We denote the body-frame coordinates by (x, y, z), the fixed-frame coordinates by (2', y, z) and choose 2 to be the symmetry axis of the cone. The tip of the cone is attached to the origin of the fixed frame, while it rolls without slipping on a horizontal surface; the Euler angle 0 = 1/2 - a is constant. a) No slipping implies a constraint y = ko between the two Euler angles. Express the constant k in terms of the given data. b) Express the system Lagrangian in terms of the generalized coordinate v. To avoid error propagation, assume the parameter k is given. You are reminded that the components of the angular velocity in the body frame are expressed in terms of Euler angles by wn = o sin 6 sin + cosŲ, W, = o sin 6 cos ' - siný, w. = o cos +. = c) Solve for y(t) and hence o(t), in terms of an initial angular velocity (0) = 1 and with (0) = 0 and 6(0) = 0.