Chasles’s (“shal’s”) theorem states that any displacement of one of these theoretical objects can be represented as a rotation plus a translation. For 10 points each:
[10m] Name these theoretical objects whose motion about a fixed point can be represented using Cayley–Klein parameters or quaternions.
ANSWER: rigid bodies [or rigid body]
[10e] When rigid body rotation is free of this quantity, the right sides of Euler’s (“OY-lurz”) equations are set to zero. This quantity is the cross product of force and the lever arm.
ANSWER: torque [prompt on tau]
[10h] Euler’s equations in vector form set this expression of L and omega, where L and omega are the angular momentum and angular velocity pseudovectors, respectively, equal to the applied torque. This expression of L and omega is derived using the relationship between time derivatives in the space and body frames.
ANSWER: L-dot plus omega cross L [or L-dot + ω × L or L-dot plus the cross product of omega and L; accept the time derivative of L (in the body frame) or dL/dT in place of “L-dot”; accept answers that flip the addition, such as omega cross L plus L-dot; reject answers that change the order of the cross product, such as “L-dot plus L cross omega”]
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