(c) The motion of a particle in a plane is governed by the Lagrangian 1 1 L = ; (x² + ÿ³) + ¿(vi – wý). (i) Obtain the equations of motion (simplify if possible). Is the force acting on the particle conservative? (ii) Verify that = Rcos t, y = Rsin t, is a solution of the equations of motion (here R is a constant). (iii) What is the general form of the solutions? Hint: The solution from part (ii) has one arbitrary constant R. The general solution includes four arbitrary constants.
(c) The motion of a particle in a plane is governed by the Lagrangian 1 1 L = ; (x² + ÿ³) + ¿(vi – wý). (i) Obtain the equations of motion (simplify if possible). Is the force acting on the particle conservative? (ii) Verify that = Rcos t, y = Rsin t, is a solution of the equations of motion (here R is a constant). (iii) What is the general form of the solutions? Hint: The solution from part (ii) has one arbitrary constant R. The general solution includes four arbitrary constants.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Repost for part iii
Transcribed Image Text:(c) The motion of a particle in a plane is governed by the Lagrangian
L = } (4² + o*) + (ut – rý).
1
1
2
2
(i) Obtain the equations of motion (simplify if possible). Is the force acting on the
particle conservative?
(ii) Verify that
x = Rcos t,
y = Rsin t,
is a solution of the equations of motion (here R is a constant).
(iii) What is the general form of the solutions?
Hint: The solution from part (ii) has one arbitrary constant R. The general
solution includes four arbitrary constants.
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