Frame b of a mechanical element.
All mechanical components are always connected together at frames. A frame is a coordinate system in the (mechanical) cut-plane of the connection point. The variables of the cut-plane are defined with respect to the corresponding frame_b and have the following meaning:
Potential variables:
S : Rotation matrix describing frame_b with respect to the inertial
frame, i.e. if ha is vector h resolved in frame_b and h0 is
vector h resolved in the inertial frame, h0 = S*ha.
r0: Vector from the origin of the inertial frame to the origin
of frame_a, resolved in the inertial frame in [m] !!! (note,
that all other vector quantities are resolved in frame_a!!!).
v : Absolute (translational) velocity of frame_a, resolved in a,
in [m/s]: v = transpose(S)*der(r0)
w : Absolute angular velocity of frame_a, resolved in a,
in [rad/s] : w = vec(transpose(S)*der(S)); Note, that
| 0 -w3 w2 |
skew(w) = | w3 0 -w1 | and w=vec(skew(w))
| -w2 w1 0 |
a : Absolute translational acceleration of frame_b - gravity
acceleration, resolved in a, in [m/s^2]:
a = transpose(S)*( der(S*v) - ng*g )
(ng,g are defined in model MultiBody.Parts.InertialSystem).
z : Absolute angular acceleration of frame_a, resolved in a,
in [rad/s^2]: z = transpose(S)*der(S*w)
Flow variables:
f : Resultant cut-force acting at the origin of frame_a,
resolved in a, in [N].
t : Resultant cut-torque with respect to the origin of frame_a,
resolved in a, in [Nm].