Math 2.0

Mechanics of particles and systems Constraints and generalized coordinates Concept

Nonholonomic system

Builds on Holonomic constraintGeneralized coordinatesVelocity

Summary

A nonholonomic system is a mechanical system with constraints on its velocities that cannot be reduced to constraints on its positions. Rolling without slipping and the blade of a skate are the standard sources of such constraints. At each instant only some directions of motion are allowed. In typical examples the system can still reach every position of a region of its configuration space. Lagrange's equations in their usual form do not apply directly, and the equations of motion need multipliers or other methods.

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Derivative, concept, no evidence levelDerivativeconceptEuclidean vector, concept, no evidence levelEuclidean vectorconceptHolonomic constraint, concept, no evidence levelHolonomic constraintconceptSmooth manifold, concept, no evidence levelSmooth manifoldconceptVelocity, concept, no evidence levelVelocityconceptConfiguration space, concept, no evidence levelConfiguration spaceconceptGeneralized coordinates, concept, no evidence levelGeneralized coordinat…conceptNonholonomic system, concept, no evidence levelNonholonomic systemconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Derivative concept
  2. Euclidean vector concept
  3. Holonomic constraint concept
  4. Smooth manifold concept
  5. Velocity concept
  6. Configuration space concept
  7. Generalized coordinates concept
  8. Nonholonomic system concept

Where this leads

4 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Nonholonomic_system
About this page
TagPTRV0QFSB9
URIm2://PTRV0QFSB9
Kindconcept
WritingW0 stub
MSC70F25, 70G45
UsesHolonomic constraint, Generalized coordinates, Velocity
Same as
Changed3 November 2026

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