MotionGenesis: F=ma Software, textbooks, training, consulting.      Vectors and vector commands

The greater-than symbol   >   denotes vectors.
For example, to multiply 2 by the   zero vector   and assign the result, type
twoTimesZeroVector> = 2 * 0>
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
 RigidBody  B 
Subsequently, other vectors may be defined in terms of these unit vectors, e.g.,
v> = 2*Ax> + 3*Ay> + 4*Az>   
w> = 6*Ax> + 7*Ay> + 8*Az>   % or  w> = Vector( A, 6, 7, 8] )    
F> = 3*Bx> + 5*By> + 7*Bz>   % or  F> = Vector( B, [3, 5, 7] ) 
MotionGenesis Get Started Vectors RigidFrame RigidBody
Input only:   VectorSampleCommands.txt
Input and output:   VectorSampleCommands.html
To multiply the vector   v>   by 5, type
vFive> = 5 * v>

To add vectors   v>   and   w>,   type

addVW> = v> + w>   

To dot-multiply   v>   with   w>,   type
Note: Since   dotVW   is a scalar, it does not end with the   >   symbol.

dotVW = Dot( v>, w> )          

To cross-multiply   w>   with   v>   and form   w> x (w> x v>)

crossWV> = Cross( w>, v> )       
crossWWV> = Cross( w>,  Cross( w>, v> ) ) 

To determine the   magnitude   and   magnitude-squared   of   v>,   type

magV = GetMagnitude( v> )      
magVSquared = GetMagnitudeSquared( v> )      

To form the unit vector in the direction of   v>,   type

unitV> = GetUnitVector( v> )  

To find the radian-measure of the angle between   v> and   w>,   type

angleBetweenVW = GetAngleBetweenVectors( v>, w> )  

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  )

To form a rotation matrix relating   Bx>, By>, Bz>   to   Ax>, Ay>, Az>, (in terms of time t)   type

B.RotateZ( A, t )

To express vector v> in terms of   Bx>, By>, Bz>,   (overwrites v>), type

Express( v>, B )

To express vector   v> + F>   in terms of   Ax>, Ay>, Az>,   type

sumInTermsOfA> = Express( v> + F>,  A )

To form the   Bx>, By>, Bz>   measures of w> (without changing w>), type

wMatrix = Vector( B, w> )

To save input (for subsequent re-use), type:   Save VectorSampleCommands.txt
To save input and output responses, type:   Save VectorSampleCommands.html

Exit the program by typing  Quit.