Engr Help

Relative Velocity and Acceleration with Translating and Rotating Frames (continued)

Since u is a unit vector d(u)/dt = ω x u and r_AB d(u)/dt = ω x r_AB u = ω x r_AB

ω x r_AB = v_AB is the velocity of point B with respect to point A in the fixed frame, F

The relative velocity equation becomes:

v_B = v_A + v_B|₁ + v_AB = v_A + v_B|₁ + ω x r_AB

Definition of terms:

where v_B is the velocity of point B in the fixed frame, F

v_A is the velocity of point A in the fixed frame, F

v_B|₁ is the velocity of B in the x₁y₁ frame (body fixed frame of reference)

v_AB is the velocity of B with respect to A in the fixed frame, F

ω is the angular velocity of body 1 in the fixed frame, F

r_AB is the position vector from A to B

Note: v_AB = ω x r_AB and r_AB