The three-dimensional motion of a particle is defined by the position vector r magnitudes of the velocity and acceleration of the particle. (The space curve described by the particle is a conic helix.) (Rt cos w„t)i + ctj + (Rt sin w„t)k. Determine the

Consider a satellite moving in a torque-free environment. The inertial frame and satellite body-fixed frame are represented by N-frame and B-frame, where {^₁, ŵ2, ñ3} and {b₁, 62, 63} are right-handed vector bases fixed in N-frame and B-frame, respectively. {1;} is aligned with the principal axis of inertia, where ☎₁ and 3 are associated with the minimum and maximum moments of inertia, respectively. Denote the satellite angular velocity by w = wib; and the inertia tensor about the CoM by Ic. Suppose that I at time t = 0 is given by: Ic(t = 0) = 2ñ₁ñ₁ +2.25 ñ¿Ñ₂ +2.25 ñ³Ñ3 – 0.75 ñ¿ñ3 −0.75 3₂ (dimensionless) Express the satellite inertia tensor about the CoM in B-frame. Determine [BN] at time t = 0, i.c., the direction cosine matrix (DCM) that represents the orientation of B-frame relative to N-frame.

The following figure shows a top view of a spinning, cylindrical gyroscope wheel. The pivot is at O, and the mass of the axle is negligible. Use ?=2.9cm and ?=3cm.  a. As seen from above, is the precession clockwise or counterclockwise?  b. If the gyroscope precesses at 1.7 revolution per second, what is the angular speed of the wheel in revolution per minute? Insert your answer correct up to at least a third decimal place.

where does the dm come from?