Can I get the solution for these Engineering physics problems? Subject is Classical Mechanics.

Textbook (required): Classical Dynamics of Particles and Systems 5th Ed., by S.T. Thornton and J.B. Marion, Cengage Learning 2012.

125% + 1) Use the Euler equation to show that the geodesic on the surface of a circular cylinder is a helix. 2) A disk of radius R rolls without slipping on a parabolic track, y=ax. a. Write down a condition for the radius R such that the disk contacts the parabola at only one point regardless of its position b. Write the equation of constraint for rolling without slipping. 3) Consider a point particle of mass m subject to the potential U = -kz. a. Write the Lagrangian for this particle in Cartesian coordinates. b. Find the equations of motion using the Lagrange method and solve them. c. What quantities are constants of the motion? 4) A particle moves in a plane under the influence of a force F = -Arr , where A and n are constants and n > 0. Choose appropriate generalized coordinates and let the potential be zero at the origin. a. Find the Lagrange equations of motion b. Show that angular momentum about the origin is conserved. c. Show that total energy is conserved