The Lagrangian Description of Motion — Lesson 3

This video focuses upon the Lagrangian description of motion. In this description, the motion of the individual particles is followed. It is shown how position vectors are used to express this motion mathematically. Parametrizing the motion of the particle using the reference position helps in capturing the motion of the particle mathematically. Lagrangian velocity is derived. Similarly, Lagrangian acceleration can be derived. A rigid body motion example is demonstrated in the video, where the body translates and rotates. Lagrangian displacement, velocity, and acceleration are shown for this example.

This type of motion where a particle motion or the motion of reference position is tracked is natural for solid mechanics. This is demonstrated by tracking the motion of two particles on the rigid body and showing that the distance between the two particles remains the same for positions before and after the motion. Eulerian description of the motion is introduced and the way in which the motion of the body is tracked in this description is completely different with respect to the Lagrangian one. In this description instead of tracking a particular point, the gaze is fixed at a particular location in the space, and instead of tracking the body, we see what happens to the material particles at that position only. The motion is defined by parametrizing the location or region at which the gaze is fixed. The concept is explained for a fluid in water. This description of motion is natural for fluids.