Question

Using the Lagrange formalism of the 2nd kind, describe the frictionless motion of a point mass confined to the surface of a cone in the field of constant gravity. (a) What is the constraint equation? m g (b) Find a coordinate transformation that automatically incorporates the constraint. Provide the Lagrange function in these coordinates. (c) Derive the equations of motion. Are there any conserved quantities and, if yes, what are they? (d) Provide a thorough qualitative discussion of the problem. Is the trajectory closed? Is it possible that the path is a horizontal circle? (Of course, alternatively you may provide a complete solution of the problem.)

          Using the Lagrange formalism of the 2nd kind,
describe the frictionless motion of a point mass
confined to the surface of a cone in the field of
constant gravity.
(a) What is the constraint equation?
m
g
(b) Find a coordinate transformation that automatically incorporates the constraint. Provide the
Lagrange function in these coordinates.
(c) Derive the equations of motion. Are there any conserved quantities and, if yes, what are they?
(d) Provide a thorough qualitative discussion of the problem. Is the trajectory closed? Is it possible
that the path is a horizontal circle? (Of course, alternatively you may provide a complete solution
of the problem.)

Using the Lagrange formalism of the 2nd kind,
describe the frictionless motion of a point mass
confined to the surface of a cone in the field of
constant gravity.
(a) What is the constraint equation?
m
g
(b) Find a coordinate transformation that automatically incorporates the constraint. Provide the
Lagrange function in these coordinates.
(c) Derive the equations of motion. Are there any conserved quantities and, if yes, what are they?
(d) Provide a thorough qualitative discussion of the problem. Is the trajectory closed? Is it possible
that the path is a horizontal circle? (Of course, alternatively you may provide a complete solution
of the problem.)

Added by Matthew J.

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