Answered: A particle of mass m is constrained to… | bartleby

Related questions

Question

A particle of mass m is constrained to move on the inside surface of a
smooth cone of half-angle a (i.e., z =r cot a) as shown in the figure to a
gravitational force. The particle is subject to a gravitational force (i.e.,
g=-gk ).
(a) Determine the Lagrangian for this particle in terms of the generalized
coordinates r and 0.
(b) Determine Lagrange's equations of motion for this particle.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Part b
. Obtain the Euler – Lagrange equation for the extremals of the functional X2 | [y2 - yy'+y'2 ]dlx X1
Consider a system spin-1/2 system, denoted by A, interacting with another system spin-1/2 system, denoted by B, such that the state of the combined system is AB) a++ B|-+). Find (a) the density matrix PA for system A corresponding to this state and (b) obtain the formulas for (()).
5. Consider the two state system with basis |+) which diagonalizes the Pauli matrix 03. Generally the state of the system at time t can be written as |W(t)) = c+(t)|+) + c_(t)|-). (i) For the Hamiltonian of the system, first take H = functions c+(t) given the initial condition that at time t = 0 Eo03. Solve for the coefficient |W(0)) = |-).
Please obtain the same result as in the book.
The Hamiltonian matrix has been constructed using an orthonormal basis. (1 1 0V (1 0 1) A = (2 1 0 )+(0 2 2 \2 1 4 where H = Hº + V and cis a constant. 1 2 0/ b) Use time-independent perturbation theory to determine the eigenvalues with corrections up to second order.