Prove that the Hamiltonian of the system is constant of motion iff potential energy doesn't depends on time explicitly?
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- Theoretical Mechanics Topic: Lagrangian and Hamiltonian Dynamics >Generate the necessary equations to this system. > Use the equations of motion >Generate equations for (x,y), (Vx,Vy), V², T > L = T-U --- For study purposes. Thank you!In a Hamiltonian system, what are the conditions for fixed points?Theoretical Mechanics Topic: Lagrangian and Hamiltonian Dynamics >Generate the necessary equations to this system. > Use the equations of motion >Generate equations for (x,y), (Vx,Vy), V², T > L = T-U --- For study purposes. Thank you!
- Let G(u, v) = (3u + v, u - 2v). Use the Jacobian to determine the area of G(R) for: (a) R = [0, 3] x [0, 5] (b) R = [2, 5] x [1, 7]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.Theoretical Mechanics Topic: Lagrangian and Hamiltonian Dynamics >Generate the necessary equations to this system. > Use the equations of motion >Generate equations for (x,y), (Vx,Vy), V², T > L = T-U --- For study purposes. Thank you!