Holonomic versus nonholonomic constraints
Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Courses in analytical mechanics for undergraduate students are often limited to treatment of holonomic constraints, which are constraints on coordinates. The concept of nonholonomic constraints, constraints on velocities, is usually only mentioned briefly and it is easy to get a wrongful idea of what they are and how to treat them. This text explains and compares the methods of deriving the Euler-Lagrange equations and the consequences when imposing different kinds of constraints. One way to properly treat both holonomic and nonholonomic constraints is given, pinpointing the difficulties and common errors. Along the way, the treatment in local coordinates is also put in more modern terms, in the language of differential geometry, which is the language most commonly used in modern texts on the subject.
Place, publisher, year, edition, pages
2012. , 42 p.
analytical mechanics, classical mechanics, lagrangian, d'alembert's principle, hamilton's principle, holonomic, nonholonomic, constraints, differential geometry, fibre bundle, curvature, falling disc
IdentifiersURN: urn:nbn:se:kau:diva-13378Local ID: FYS C-2OAI: oai:DiVA.org:kau-13378DiVA: diva2:528335
Subject / course
2012-05-22, 21D304, Karlstads universitet, Karlstad, 10:15 (English)
UppsokPhysics, Chemistry, Mathematics
Fuchs, Jürgen, Professor
Uggla, Claes, Professor