Math 2.0

Mechanics of particles and systems Constraints and generalized coordinates Concept

Generalized coordinates

Builds on Configuration spaceHolonomic constraint

Summary

Generalized coordinates are numbers q1,…,qnq_1, \dots, q_n that fix the position of a mechanical system and can be varied independently of each other. They are local coordinates on the configuration space, chosen so that the holonomic constraints hold automatically. Angles, lengths and other convenient parameters can serve, not only Cartesian coordinates. Lagrangian and Hamiltonian mechanics write the equations of motion in generalized coordinates.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

Show the path as a graph
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…concept
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. Holonomic constraint concept
  2. Smooth manifold concept
  3. Configuration space concept
  4. Generalized coordinates concept

Where this leads

32 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Generalized_coordinates
About this page
TagBCF1EX9W2M
URIm2://BCF1EX9W2M
Kindconcept
WritingW0 stub
MSC70G10, 70H03
UsesConfiguration space, Holonomic constraint
Same as
Changed3 November 2026

Markdown · JSON · Edit on GitHub

What this page needs for W1

  • an inventory row: the row of the inventory that the node accounts for (0 of 1)
  • a source with a locator (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

Used by

Definitions