Spring 2003 16.614-4 This final expression looks messy, but it is really just two nested versions of what we have seen before The nesting can continue to more levels and can be automated Note that this type of expression is very easy to get wrong if not done carefully and systematically The hardest term to capture here is the 2wx(2wx3r)which comes from the2(1d×P11 )term Plr is the relative velocity of P with respect to the origin of frame 1 as seen by an observer in the rotating frame Example: acceleration of the tip of the tail rotor on a helicopter The helicopter body is rotating The tail rotor is rotating as well, but the base is attached to the odVSpring 2003 16.61 4–4 • This final expression looks messy, but it is really just two nested versions of what we have seen before. – The nesting can continue to more levels and can be automated. • Note that this type of expression is very easy to get wrong if not done carefully and systematically. – The hardest term to capture here is the 21
ω × (2
ω × 3
r ) which comes from the 2(1
ω × P1 ˙
r 1 ) term. – P1 ˙
r 1 is the relative velocity of P with respect to the origin of frame 1 as seen by an observer in the rotating frame 1. • Example: acceleration of the tip of the tail rotor on a helicopter: – The helicopter body is rotating. – The tail rotor is rotating as well, but the base is attached to the body