A double pendulum consists of two simple pendula, with one pendulum suspended from the bob of the other. If the two pendula have equal lengths and have bobs of equal mass and if both pendula are confined to move in the same plane, find Lagrange's equations of motion for the system. Do not assume small angles.
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- Determine the motion expressions for each of the systems shown below by using the Euler-Lagrange equation. not skiping steps please explain i do not understand yet A block of mass m that slides frictionlessly on an inclined plane tied to an ideal spring of constant k as shown in the figureI just need help for part a. Question 3. (Hamilton and Lagrange formalism)Explain the physical significance of the Hamiltonian under what conditions can Hamiltonian be identified as the total energy of the system ?
- (d) Show that the position operator (f = x) and the hamiltonian operator (H = -(n2/2m)d² /dx2 + V(x)) are hermitian. %3DProblem 3 A ball of mass m, slides over a sliding inclined plane of mass M and angle a. Denote by X, the coordinate of O' with re- m spect to 0, and by (x.y) the Coordinate of m with respect M a O' to O'(see figure below) 1. Calculate the degree of freedom of the system 2. Find the velocity of m with respect to O. 3. Write the expression of the Lagrangian function 4. Derive the Euler Lagrange equations 5. Find z" and X" in ters of the masses (m,M), angle a and gFind the degrees of freedom in each of the following situations. Fully justify your answer. a. Consider a bead that is threaded on a rigid circular hoop of radius R lying in the XY-plane with its center at O. b. A particle is confined to move on the surface of a circular cone with its axis on the z-axis, vertex at the origin (pointing down), and half-angle a. C. A simple planar pendulum is suspended from the roof of a railroad car that is being forced to oscillate back and forth so that the point of suspension of the pendulum from the roof has a sinusoidal position dependence with respect to the horizontal position coordinate.
- 1Theoretical 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!M.r Mg(r- a), write the system's Lagrang ian is L = (")(*² + r²o²) + 3. If a Hamiltonian of this sy stem, and find conservative and cyclic variables. 4. Calculate y(x) function which gives the stationary value of (y²+y')dx.