Where \ Omega is the order of the harmonics to be estimated, \ Theta is the total angular rotation of the shaft in the acquisition window, \ theta and \ omega are respectively the instantaneous angular rotation and velocity of the reference shaft.
12.
Note : To use the equation as written above ( with the leading 0.620 ), certain units must be used with the parameters listed ( e . g . radians per second for angular rotation, NOT radians or revolutions per minute ).
13.
Given the radius " R " of the turntable in that animation, the rate of angular rotation ?, and the speed of the cannonball ( assumed constant ) " v ", the correct angle ? to aim so as to hit the target at the edge of the turntable can be calculated.
14.
R is a unit vector pointing from the axis of rotation to one of the spheres, and "'? "'is a vector representing the angular rotation, with magnitude ? and direction normal to the plane of rotation given by the right-hand rule, " m " is the mass of the ball, and " R " is the distance from the axis of rotation to the spheres ( the magnitude of the displacement vector, | "'x "'
15.
Where the angular rotation of the frame is expressed by the vector "'? "'pointing in the direction of the axis of rotation, and with magnitude equal to the angular rate of rotation " ? ", symbol ?denotes the vector cross product, vector "'x " "'B " locates the body and vector "'v " "'B " is the velocity of the body according to a rotating observer ( different from the velocity seen by the inertial observer ).
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