1. Hour 17 Lagrangian Dynamics
Physics 321
Hour 17
Lagrangian Dynamics

2. Lagrangian Strategy Determine the number of degrees of freedom
Write down T and U in terms of convenient coordinates
Write equations of constraint – constraints between variables
Be sure the variables left are independent of each other
Use 𝜕ℒ 𝜕𝑞 = 𝑑 𝑑𝑡 𝜕ℒ 𝜕 𝑞
Add friction and “lossy” forces by hand

3. Outline Calculus of Variations One variable Two variables
Ball on block with spring(.nb)
Choosing coordinates
Wheel with spring (.nb)
Ignorable varaibles
Adding drag forces
Bowl
Tricky T
Atwood Machine I

4. Examples
ball on block.nb
springwheel.nb