Book contents
- Frontmatter
- Contents
- Preface
- Notation
- 1 Introduction
- 2 Geometric algebra in two and three dimensions
- 3 Classical mechanics
- 4 Foundations of geometric algebra
- 5 Relativity and spacetime
- 6 Geometric calculus
- 7 Classical electrodynamics
- 8 Quantum theory and spinors
- 9 Multiparticle states and quantum entanglement
- 10 Geometry
- 11 Further topics in calculus and group theory
- 12 Lagrangian and Hamiltonian techniques
- 13 Symmetry and gauge theory
- 14 Gravitation
- Bibliography
- Index
3 - Classical mechanics
Published online by Cambridge University Press: 05 January 2013
- Frontmatter
- Contents
- Preface
- Notation
- 1 Introduction
- 2 Geometric algebra in two and three dimensions
- 3 Classical mechanics
- 4 Foundations of geometric algebra
- 5 Relativity and spacetime
- 6 Geometric calculus
- 7 Classical electrodynamics
- 8 Quantum theory and spinors
- 9 Multiparticle states and quantum entanglement
- 10 Geometry
- 11 Further topics in calculus and group theory
- 12 Lagrangian and Hamiltonian techniques
- 13 Symmetry and gauge theory
- 14 Gravitation
- Bibliography
- Index
Summary
In this chapter we study the use of geometric algebra in classical mechanics. We will assume that readers already have a basic understanding of the subject, as a complete presentation of classical mechanics with geometric algebra would require an entire book. Such a book has been written, New Foundations for Classical Mechanics by David Hestenes (1999), which looks in detail at many of the topics discussed here. Our main focus in this chapter is to areas where geometric algebra offers some immediate benefits over traditional methods. These include motion in a central force and rigid-body rotations, both of which are dealt with in some detail. More advanced topics in Lagrangian and Hamiltonian dynamics are covered in chapter 12, and relativistic dynamics is covered in chapter 5.
Classical mechanics was one of the areas of physics that prompted the development of many of the mathematical techniques routinely used today. This is particularly true of vector analysis, and it is now common to see classical mechanics described using an abstract vector notation. Many of the formulae in this chapter should be completely familiar from such treatments. A key difference comes in adopting the outer product of vectors in place of the cross product. This means, for example, that angular momentum and torque both become bivectors.
- Type
- Chapter
- Information
- Geometric Algebra for Physicists , pp. 54 - 83Publisher: Cambridge University PressPrint publication year: 2003