Рет қаралды 3,309
** NOTE: θ1 is measured relative to r2 and NOT relative to the vertical ** - VIEW: bit.ly/3VhnRP7
Deriving the equation of motion for a ball rolling down the side of a cylinder using the Method of Lagrange Multipliers and determining the point at which the ball leaves the surface.
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CHAPTERS:
0:00 Introduction
0:10 Set Up
2:10 Questions
3:08 Constraint Equation
3:45 Kinetic Energy
4:39 Digression
8:15 Potential Energy
8:36 The Extended Lagrangian
9:48 Lagrange's Equation
12:07 What is the Lagrange Multiplier?
17:54 Equation of Motion
20:55 When Does the Ball Lose Contact?
21:35 Integrating the Equation of Motion
24:42 Initial Conditions
26:25 Finding the Point
27:17 Review
29:06 Outtro