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.
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Q: 3.1 Distinguish between the following approaches for solving problems. 3.1.1 The method of applying…
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- 1.What is Hamiltons canonical equations of motion 2.also show total energy conservedFor a 1 particle stationary state system in three dimensions,. O 6 Hamiltonian equations of motion are necessary. 6 Lagrangian equations of motion are necessary. 6 Newtonian equations of motion are necessary. O none of the aboveI just need help for part a. Question 3. (Hamilton and Lagrange formalism)
- 4Problem 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 gLagrangian Dynamics Ep = 0 A pendulum of length / and mass m is mounted on a block of mass M. The block can move freely without friction on a horizontal surface as shown in the adjacent figure H. 1. Find the velocity of mass m, w.r.t the origin O 2. Write the Lagrangian of the system 3. Derive the Euler Lagrange equations
- This is question 8.8 in John R. Taylor's "Classical Mechanics" textbook by the way! (ISBN: 9781891389221)Consider the motion of a point charge q in an electromagnetic field. Let Ē and 3 be the electric and magnetic fields, respectively, which can be derived from a scalar potential and a vector potential A Əà Ē=-V6- - Ət Use the potential energy given by V(r) = 94 - 9(÷ F). a. What is the lagrangian in terms of r? b. What is the conjugate momentum vector p. ? Show your solution. B = V X ATheoretical 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!