Particles and Space Curves

  • Oliver M. O’Reilly


In this chapter we discuss the differential geometry of space curves (a curve embedded in Euclidean three-space ε3). In particular, we introduce the Serret-Frenet basis vectors e t ,e n ,e b . This is followed by the derivation of an elegant set of relations describing the rate of change of the tangent e t , principal normal e n , and binormal e b vectors. Several examples of space curves are then discussed. We end the chapter with some applications to the mechanics of particles. Subsequent chapters will also discuss several examples.


Tangent Vector Position Vector Space Curve Plane Curve Space Curf 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Oliver M. O’Reilly
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA

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