Help in understanding this derivation of Lagrange Equations in Non-Holonomic case

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In summary, the derivation of Lagrange equations in the non-holonomic case involves adapting the traditional Lagrangian mechanics framework to systems with non-integrable constraints. This requires incorporating generalized coordinates and velocities, along with the use of Lagrange multipliers to account for the constraints. The resulting equations describe the dynamics of the system while respecting the limitations imposed by non-holonomic conditions, enabling the analysis of more complex mechanical systems.
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Kashmir
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I dont Understand how we get the final equations relating ##Q_r## with ##\lambda## given the conditions above?
 
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