Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Physics LibreTexts

Search

  • Filter Results
  • Location
  • Classification
    • Article type
    • Author
    • Embed Hypothes.is?
    • Embebbed CalcPlot3D?
    • Cover Page
    • License
    • Show TOC
    • Transcluded
    • OER program or Publisher
    • Student Analytics
    • Autonumber Section Headings
    • License Version
    • Print CSS
      • Screen CSS
      • PrintOptions
    • Include attachments
    Searching in
    About 2 results
    • 15.3: Canonical Transformations in Hamiltonian Mechanics
      https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/15%3A_Advanced_Hamiltonian_Mechanics/15.03%3A_Canonical_Transformations_in_Hamiltonian_Mechanics
      Hamiltonian mechanics is an especially elegant and powerful way to derive the equations of motion for complicated systems. Integrating the equations of motion to derive a solution can be a challenge. ...Hamiltonian mechanics is an especially elegant and powerful way to derive the equations of motion for complicated systems. Integrating the equations of motion to derive a solution can be a challenge. Hamilton recognized this difficulty, so he proposed using generating functions to make canonical transformations which transform the equations into a known soluble form.
    • 10.2: General and Canonical Transformations
      https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Graduate_Classical_Mechanics_(Fowler)/10%3A_Canonical_Transformations/10.02%3A_General_and_Canonical_Transformations
      Q_{i}=Q_{i}\left(p_{i}, q_{i}, t\right), \quad P_{i}=P_{i}\left(p_{i}, q_{i}, t\right) \dot{Q}_{i}=\partial H^{\prime} / \partial P_{i}, \quad \dot{P}_{i}=-\partial H^{\prime} / \partial Q_{i}, \text ...Q_{i}=Q_{i}\left(p_{i}, q_{i}, t\right), \quad P_{i}=P_{i}\left(p_{i}, q_{i}, t\right) \dot{Q}_{i}=\partial H^{\prime} / \partial P_{i}, \quad \dot{P}_{i}=-\partial H^{\prime} / \partial Q_{i}, \text { for the new } H^{\prime}(P, Q) .

    Support Center

    How can we help?