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 \( \mathbb{E}^3 \)). In particular, we introduce the Serret-Frenet basis vectors \( \left\{ {{\bf e}_t, {\bf e}_n, {\bf e}_b } \right\} \). This is followed by the derivation of an elegant set of relations describing the rate of change of the tangent et, principal normal en, and binormal eb vectors. Several examples of space curves are then discussed. We end the chapter with some applications to the mechanics of particles.


Position Vector Space Curve Plane Curve Space Curf Roller Coaster 
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Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of California, BerkeleyBerkeleyUSA

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