Question 10.11: Drawing a velocity diagram 2 Two rigid rods C D and DE, of l...

Classical Mechanics

Drawing a velocity diagram 2

Two rigid rods C D and DE, of lengths 2a and 2b, are flexibly jointed at D and can move freely on a horizontal table. Choose generalised coordinates and draw a velocity diagram for this system.

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Let Oxy be a system of Cartesian coordinates in the plane of the table. Let (X, Y ) be the Cartesian coordinates of the centre of the rod C D, and let θ and Φ be the angles that the two rods make with positive x-axis. Then X, Y , θ, Φ are a set of generalised coordinates for this system. These coordinates, and the corresponding velocity diagram are shown in Figure 10.10. There are four contributions to the velocity of the centre of the rod DE. Also, each rod has an angular velocity.

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