Math 2.0

Mechanics of particles and systems Constraints and generalized coordinates Concept

Generalized force

Builds on Generalized coordinates

Summary

A generalized force is the component of the applied forces along one generalized coordinate. It is defined so that the work of the forces in a small change δq\delta q of the coordinates is ∑iQi δqi\sum_i Q_i\, \delta q_i. Generalized forces appear on the right-hand side of Lagrange's equations. If the coordinate is a length the generalized force is a force, and if it is an angle the generalized force is a torque.

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Holonomic constraint, concept, no evidence levelHolonomic constraintconceptSmooth manifold, concept, no evidence levelSmooth manifoldconceptConfiguration space, concept, no evidence levelConfiguration spaceconceptGeneralized coordinates, concept, no evidence levelGeneralized coordinat…conceptGeneralized force, concept, no evidence levelGeneralized forceconcept
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  1. Holonomic constraint concept
  2. Smooth manifold concept
  3. Configuration space concept
  4. Generalized coordinates concept
  5. Generalized force concept

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15 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Generalized_forces
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Tag9WQT2RMGTZ
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WritingW0 stub
MSC70G10, 70H03
UsesGeneralized coordinates
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Changed3 November 2026

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