Transcript Physics 321 Hour 17 Lagrangian Dynamics

Physics 321
Hour 17
Lagrangian Dynamics
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 𝜕ℒ
𝑑𝑡 𝜕𝑞
• Add friction and “lossy” forces by hand
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
Examples
ball on block.nb
springwheel.nb