Discussion Overview
The discussion focuses on the existence of explicit equations of motion for non-holonomic systems, contrasting them with holonomic cases. Participants explore the treatment of non-holonomic constraints within the framework of Lagrangian mechanics, seeking a general form of the equations of motion rather than specific examples or established methods.
Discussion Character
- Technical explanation
- Debate/contested
Main Points Raised
- One participant notes that while holonomic systems allow for straightforward application of the Lagrangian in deriving equations of motion, the same may not hold for non-holonomic systems.
- Another participant suggests consulting Landau and Lifshitz for insights on non-holonomic constraints, emphasizing the need for proper introduction of Lagrange multipliers.
- A participant expresses disappointment in the limited treatment of non-holonomic constraints in Landau's work, indicating a desire for a more comprehensive understanding beyond standard methods.
- Some participants argue that the final form of the equations of motion for non-holonomic systems is inherently tied to the local nature of these constraints, which cannot be resolved merely by selecting independent coordinates.
- There is a suggestion that while Lagrange equations are a necessary step, they must be solved in conjunction with non-holonomic constraint equations, raising the question of whether a general explicit formulation exists.
Areas of Agreement / Disagreement
Participants express differing views on the availability and clarity of general equations for non-holonomic systems. While some assert that the final forms exist, others question their comprehensiveness and accessibility in existing literature.
Contextual Notes
Participants highlight limitations in the treatment of non-holonomic constraints in standard texts, indicating a potential gap in the literature regarding explicit formulations. The discussion remains focused on theoretical aspects without resolving the existence of a universally accepted general form.