7-15. A pendulum consists of a mass m suspended by a massless spring with unextended length b and spring constant k. Find Lagrange's equations of motion.
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- Explain the physical significance of the Hamiltonian under what conditions can Hamiltonian be identified as the total energy of the system ?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!
- 3.1 Distinguish between the following approaches for solving problems. 3.1.1 The method of applying Newton's second law from the Lagrangean method. 3.1.2 The method of applying the Lagrangean from the Hamiltonian method.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!Q1. A particle of mass m is moving in a central potential V that does not depend on velocity. Set up Hamiltonian and try different quantities Poisson bracket with the Hamiltonian to find if they are constants (integrals) of motion. Solve (i) [pr, H] (ii) [po, H] (iii) [p3, H] (iv) [p² + P² sin² 0 ) H]