Introduction to Classical Mechanics · Problem 6.37

The Lagrangian method — Morin

Physics — Mechanics · forces-of-constraint

Problem

Cartesian coordinates ** In Eq. (6.35), take two time derivatives of the

\sqrt{x^2 + y^2} - R = 0

equation to obtain

R^2(x\ddot{x} + y\ddot{y}) + (x\dot{y} - y\dot{x})^2 = 0,

and then combine this with the other two equations to solve for

F

in terms of

x

y

\dot{x}

\dot{y}

. Convert the result to polar coordinates (with

\theta

measured from the vertical) and show that it agrees with Eq. (6.32).