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:
RigidFrame A RigidBody B 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] ) |
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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.