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Vectors and vector commands
To create sets of right-handed orthogonal unit vectors:
Ax>, Ay>, Az>   fixed in a reference frame A, and
Bx>, By>, Bz>   fixed in a rigid body B, type
RigidFrame A % Creates Ax>, Ay>, Az> RigidBody B % Creates Bx>, By>, Bz>
The greater-than symbol  >  denotes vectors. For example,  0>  denotes the zero vector.
Subsequently, other vectors may be defined in terms of these unit vectors, e.g.,
v> = 2*Ax> + 3*Ay> + 4*Az> w> = 5*Ax> + 0*Ay> + 6*Az> % or w> = Vector( A, 5, 0, 6] ) F> = 0*Bx> + 7*By> + 8*Bz> % or F> = Vector( B, [0, 7, 8] )
To multiply the vector  v>  by 5, type
vFive> = 5 * v> -> vFive> = 10*Ax> + 15*Ay> + 20*Az>
To add vectors  v>  and  w>,  type
addVW> = v> + w> -> addVW> = 7*Ax> + 3*Ay> + 10*Az>
To dot-multiply  v>  with  w>,  type
dotVW = Dot( v>, w> ) % dotVW is a scalar so its name does not use  > -> dotVW = 34
To cross-multiply  w> with  v>  and subsequently form   w> x (w> x v>)
crossWV> = Cross( w>, v> ) -> crossVW> = -18*Ax> - 8*Ay> + 15*Az> crossWWV> = Cross( w>, Cross( w>, v> ) ) -> crossWWV> = 48*Ax> - 183*Ay> - 40*Az>
To determine the magnitude and magnitude-squared of  v>,  type
magV = GetMagnitude( v> ) -> magV = 5.385165 magVSquared = GetMagnitudeSquared( v> ) -> magVSquared = 29
To form the unit vector in the direction of  v>,  type
unitV> = GetUnitVector( v> ) -> unitV> = 0.3713907*Ax> + 0.557086*Ay> + 0.7427814*Az>
To find the radian-measure of the angle between  v> and  w>,  type
angleBetweenVW = GetAngleBetweenVectors( v>, w> ) -> angleBetweenVW = 0.6294032
To form the ordinary time-derivative of the vector  t*v> + sin(t)*w>,  in reference frame A, type
vectorDerivative> = Dt( t*v> + sin(t)*w>, A ) -> vectorDerivative> = (2+5*cos(t))*Ax> + 3*Ay> + (4+6*cos(t))*Az>
To form a rotation matrix relating  Bx>, By>, Bz>  to  Ax>, Ay>, Az>  (in terms of time t),  type
B.SetRotationMatrixZ( A, t ) -> B_A = [cos(t), sin(t), 0; -sin(t), cos(t), 0; 0, 0, 1]
To express vector v> in terms of  Bx>, By>, Bz>,  type
Express( v>, B ) -> v> = (2*cos(t)+3*sin(t))*Bx> + (3*cos(t)-2*sin(t))*By> + 4*Bz>
To express the vector  w> + F>  in terms of  Ax>, Ay>, Az>,  type
addWFInTermsOfAxyz> = Express( w> + F>, A ) -> addWFInTermsOfAxyz> = (5-7*sin(t))*Ax> + 7*cos(t)*Ay> + 14*Az>
To form the  Bx>, By>, Bz>,  measures of w>, type
wMatrix = Vector( B, w> ) -> wMatrix = [5*cos(t); -5*sin(t); 6]
To save commands (for subsequent re-use) or commands/responses, type
Save MGVectorExample.txt % Save commands. Save MGVectorExample.html % Save commands and responses.
Exit the program by typing Quit.
MotionGenesis™ also does matrix algebra and solves sets of linear equations or nonlinear equations, and ODEs (ordinary differential equations).