Hour 17 Lagrangian Dynamics

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Presentation transcript:

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 𝑑𝑡 𝜕ℒ 𝜕 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