YoVDO

The Frenet Serret Equations - Differential Geometry

Offered By: Insights into Mathematics via YouTube

Tags

Geometry Courses Torsion Courses Differential Geometry Courses Curvature Courses

Course Description

Overview

Explore the Frenet Serret equations in this comprehensive differential geometry lecture. Delve into the mathematical description of unit speed space curves twisting and rotating in three-dimensional space using vector-valued derivatives. Learn about the triple of unit vectors T, N, and B (tangent, normal, and bi-normal) that form a mutually perpendicular frame of basis vectors at each point of the curve. Discover how curvature and torsion play crucial roles in describing the curve's behavior as it moves through space. Gain insights into topics such as normalization, vector quantities, osculating circles, and the Frenet frame. This in-depth exploration of space curves and their properties provides a solid foundation for understanding complex geometric concepts in three-dimensional space.

Syllabus

Introduction
Curvature
General curvature
Normalization
Curves
Vector quantities
Useful lemma
Space curves
Renormalization
Osculating Circle
oscillating plane
third vector
frenet frame
frenet equations
b prime
n prime


Taught by

Insights into Mathematics

Related Courses

Elements of Structures
Massachusetts Institute of Technology via edX
材料力學一 (Mechanics of Materials (1))
National Taiwan University via Coursera
Mechanics of Materials II: Thin-Walled Pressure Vessels and Torsion
Georgia Institute of Technology via Coursera
Solid Mechanics
Indian Institute of Technology Delhi via Swayam
Strength Of Materials
Indian Institute of Technology, Kharagpur via Swayam