What is a degree of freedom? Configuration spaces and their topology Articles uri icon

publication date

  • October 2024

start page

  • 743

end page

  • 751

issue

  • 10

volume

  • 92

International Standard Serial Number (ISSN)

  • 0002-9505

Electronic International Standard Serial Number (EISSN)

  • 1943-2909

abstract

  • Understanding degrees of freedom in classical mechanics is fundamental to characterizing physical systems. Counting them is usually easy, especially if we can assign them a clear meaning. However, the precise definition of a degree of freedom is not usually presented in first-year physics courses since it requires mathematical knowledge only learned in more advanced courses. In this paper, we use a pedagogical approach motivated by simple but non-trivial mechanical examples to define degrees of freedom and configuration spaces. We highlight the role that topology plays in understanding these ideas.

subjects

  • Mechanical Engineering
  • Physics

keywords

  • double pendulum; electromagnetism; mechanical systems; harmonic oscillator; gauge freedom; classical mechanics; robotics; topological invariant; general topology; geometry (mathematics)