Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
Q.5) A particle is suspendended from a support by a light inextensible string which passes through a small fixed ring vertically below the support. The particle moves in a verticle plane with the string taut. At the same time, the support is made to move verticall having an upward displacement ((t) at time t. The effect is t hat the particle oscillates like a simple pendulum whose string at time t is a - ((t), where a is a positive const ant. Show that the Lagrangian is 1 L = m (a - s)*ở? + ¢²) + mg(a – () cos 0, where 0 is the angle between the string and the downward vertical. Find the Hamilt onian and obtain Hamiltonian's equations. Is H conserved.? Solution:-

Q.5) A particle is suspendended from a support by a light inextensible string which passes through a small fixed ring vertically below the support. The particle moves in a verticle plane with the string taut. At the same time, the support is made to move verticall having an upward displacement ((t) at time t. The effect is t hat the particle oscillates like a simple pendulum whose string at time t is a - ((t), where a is a positive const ant. Show that the Lagrangian is 1 L = m (a - s)*ở? + ¢²) + mg(a – () cos 0, where 0 is the angle between the string and the downward vertical. Find the Hamilt onian and obtain Hamiltonian's equations. Is H conserved.? Solution:-

icon
Related questions
Question
Q.5) A particle is suspendended from a support by a light inextensible string which passes through a small fixed ring vertically below the support. The particle moves in a verticle plane with the string taut. At the same time, the support is made to move vert icall having an upward displacement ((t) at time t. The effect is that the particle oscillates like a simple pendulum whose string at time t is a – 5(t), where a is a positive const ant. Show that the Lagrangian is 1 m (a - S)0? + ¿²) + mg(a – () cos 0, where 0 is the angle between the string and the downward vertical. Find the Hamilt onian and obtain Hamiltonian's equations. Is H conserved.? Solution:-
Transcribed Image Text:Q.5) A particle is suspendended from a support by a light inextensible string which passes through a small fixed ring vertically below the support. The particle moves in a verticle plane with the string taut. At the same time, the support is made to move vert icall having an upward displacement ((t) at time t. The effect is that the particle oscillates like a simple pendulum whose string at time t is a – 5(t), where a is a positive const ant. Show that the Lagrangian is 1 m (a - S)0? + ¿²) + mg(a – () cos 0, where 0 is the angle between the string and the downward vertical. Find the Hamilt onian and obtain Hamiltonian's equations. Is H conserved.? Solution:-
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer