Lagrangian of particle and lagranges equations of motion

Assignment Help Physics

Reference no: EM13536956

Consider a particle of mass m moving in a vertical x-y plane along a curve y=acos(2xπ/λ). free fall acceleration is g. First consider two coordinates x and y:

a) write down lagrangian of system

b) obtain lagrange's equation of motion with undetermined multipliers.

c) define the forces of the constraint. what is the minimal velocity of a particle at the top of a curve when the force of constrain vanishes? compare your expressions for the forces of constraint with the forces you would introduce to formulate the problem in terms of newtons second law.

Now choose a single generalized coordinate corresponding to a horizontal coordinate x.

d) write down the lagrangian of the particle and lagrange's equations of motion.

e) Define the generalized momentum and write down the hamiltonian of the particle.

f) derive the canonical(Hamilton's) equation of motion.

g) demonstrate that the canonical equations of motions can be reduced to lagrange's equation of motion.

Reference no: EM13536956

Questions Cloud

Use amperes law to determine the magnetic field : Use Ampere’s law to determine the magnetic field in a densely wound toroidal solenoid with inner radius a, outer radius b, and N total turns. The cross section of the solenoid is a rectangle of width b-a and height h.

The atoms of a carbon dioxide molecule : The atoms of a carbon dioxide molecule (C02) are arranged in a line, with the carbon in the center and the oxygens on either side at a distance of 0.116 nm. In the absence of vibrations, calculate the energy (in micro electronvolt) of the third ro..

Neglect the mass of the cable : A mine elevator is supported by a single steel cable 2.8 cm in diameter. The total mass of the elevator cage and occupants is 520 kg. By how much does the cable stretch when the elevator hangs by (a) 13 m of cable and (b) 364 m of cable? (Neglect the..

Calculate the strain the stress : After a fall, a 96 kg rock climber finds himself dangling from the end of a rope that had been 17 m long and 9.9 mm in diameter but has stretched by 3.1 cm. For the rope, calculate (a) the strain, (b) the stress, and (c) the Young's modulus.

Lagrangian of particle and lagranges equations of motion : Consider a particle of mass m moving in a vertical x-y plane along a curve y=acos(2xπ/λ). free fall acceleration is g. First consider two coordinates x and y:

Find the energy of the second excited vibrational state : The effective vibrational force constant of CN is 1.017 x 104 eV/nm2. Relative to the ground state, find the energy of the second excited vibrational state.

Consider a parallel plate capacitor with an area : Consider a parallel plate capacitor with an area of 2 cm^2 and a plate separation of 0.02 mm which is charged to a voltage of 2 kV. The work function for the electrons in the plate is 3.8 eV. Compare the electron tunneling current when there is a vac..

How much energy was stored in the spring : A block of mass M = 1.00 kg contains a coiled spring and a ball of mass m = .250 kg. The spring is released when the ball block system is at rest on the edge of a frictionless plane inclined 20 degrees from the horizontal. The ball, initially 2.00..

What is the instantaneous AC current : A circuit contains only a(n) 0.219 H inductor. An AC voltage of peak value 163 V and frequency 61.3 Hz is applied to the circuit. When the instantaneous voltage is 163 V, what is the instantaneous AC current?

User Account

All Pages