Explain the physical significance of the Hamiltonian under what conditions can Hamiltonian be identified as the total energy of the system ?
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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!a) Define a conservative system and state how the lagrange's equations are modified b) State three advantages why Lagrangian approach to solving problems is more superior compared to Newtonian approach c) Use Lagrange's equation to obtain the equations of motion of a linear harmonic oscillator (Hint: the system is conservative)In a Hamiltonian system, what are the conditions for fixed points?
- 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.Q1