spacecurves Tag Posts Index

The TNB Frame: Normal and Osculating Planes + Example on a Circular Helix

In this video, I go over the TNB Frame for space curves and their associated Normal and Osculating Planes, which have applications in the motion of spacecraft. The

Normal and Binormal Vectors + Example on a Circular Helix

In this video, I go over the principal unit normal and binormal vectors of a space curve, which are both derived from the unit tangent vector. Since the unit tangent

Arc Length of a Space Curve + Example on Circular Helix

In this video, I extend the formula for the arc length of a 2D plane curve to that of a 3D space curve, both of which can be represented in compact form as the integral

Plane Curves as Vector Functions and the Structure of a DNA Helix

In this video I discuss how plane curves can be represented as vector functions, and illustrate an example of a plane curve that spirals upwards into a helix. YouTube

Space Curves: Tracing out the Tip of a Continuous Vector Function

In this video I show that a continuous vector function in 3D forms a curve in space when tracing out the point on the tip of the vector as it moves in time. Note