8 Given a material point P(r,m) which moves on the plane Ax+By+Cz = D sub the effect of its weight. Determine the Lagrange function of system, the Lagrange equations and the equations of motion. Also to be found generalized forces.

Anil

A massless spring with equilibrium length d and spring constant k connects two particles. The system is flat and horizontal, yet it may spin and vibrate (ccompress\stretch).1- Determine the system's Lagrangian.2- Determine the system's Hamiltonian.3- Calculate Hamilton's equations of motion. It should be noted that the generalized momenta can be omitted. -It is worth noting that as the mass spins, it begins to expand. Hint: make your coordinate system's origin the center of the unstretched spring.  also In generalized coordinates of (r_i) and (theta_i) , express your equations.

Q1