Aball of mass m moves along a thread that rotates around one end at an angular velocity ω. The thread is at an angle α with respect to the axis of rotation. Using Lagrange's equations, find the equations of motion of mass along the thread and the time it takes for the ball to slide with nor if it starts from a state of rest at the top. b) Find the curve that connects two points in a plane and its length is the smallest

Aball of mass m moves along a thread that rotates around one end at an angular velocity ω. The thread is at an angle α with respect to the axis of rotation. Using Lagrange's equations, find the equations of motion of mass along the thread and the time it takes for the ball to slide with nor if it starts from a state of rest at the top. b) Find the curve that connects two points in a plane and its length is the smallest

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.6P

See similar textbooks

Similar questions

A particle P of mass 2m can slide along a smooth rigid straight wire. The wire has one ofits points fixed at the origin ’O’, and is made to rotate in a plane through ’O’ with constantangular speed Ω. Show that r , the distance of P from O, satisfies the equation r ̈ − (Ω^2)*r = 0 Initially, P is at rest (relative to the wire) at a distance a from O. Find r as a function of t in the subsequent motion.
ELEMENTARY APPLICATION OF DE/LINEAR DE OF ORDER, n, Case 1 and 2
Consider the coordinate system in the diagram bellow; the z axis points out of the page. At the point (-d, 0, 0) a ball of mass m is initially (at t= 0) at rest, but it is dropped under the face of gravity, near the Earth. We ignore air resistance as usual, and treat ball as a point mass. 1.c) What is the angular momentum relative to the origin of the coordinate system?
Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite? Let T denote the period of revolution of the satellite. Kepler’s third law says that the square of T is proportional to the cube of the major semiaxis a of its elliptical orbit. In particular, if GM D 1, then?
. Consider a system of N particles in a uniform gravitational field. Prove that the total gravitational torque about center of mass(CM) is zero.?
Hi, can you please help me with this assignment A pendulum of length L. A ball that practically carries all the weightpendulum, has a velocity of velocity v1 at the moment when the cord makes an angle \phi_1 with the vertical direction.a) Derive the relation for the velocity of the ball at the lowest point of its trajectory (\phi = 0deg).What is the smallest possible value of velocity v1 for the pendulum tob) reach a position in which the massless cord is in horizontal position \phi=90deg,c) pass the highest point above the pivot so that the cord does not kink (\phi = 180deg+)? Thank You
Get the resultant in x and y. Also the θ. Show the complete and step by step solution. It is a Static of Rigid Bodies subject.
If the rigid body rotates 30deg about the global X-axis and the origin of the body translates to (X, Y, Z)=(500, 0 600), the final point in the Global frame is (500 -100, 773.2). Find the origin position (x1, y1, z1) in the body coordinate frame by using the inverse 4X4 matrix.
show complete solution and free body diagrams
Consider a vector Q that rotates at angular frequency ω about some fixed axis of rotation (~ω).Further, Q is at a fixed angle α relative to that axis. Show that the time rate of change of Q is given by
Consider a satellite of mass m moving in a circular orbit around the Earth at a constant speed v and at an altitude h above the Earth’s surface as illustrated as shown. (A) Determine the speed of the satellite in terms of G, h, RE (the radius of the Earth), and ME (the mass of the Earth).
If a particle be describing an ellipse about a centre of force in the centre, show that the sum of the reciprocates of its angular velocities about foci is constant.