/FRAME/MOV2

Block Format Keyword Describes moving frames. Relative motion with respect to a reference frame. Moving frame definition differs from /FRAME/MOV. 8

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/FRAME/MOV2/frame_ID
frame_title
node_ID1 node_ID2 node_ID3

Definition

Field Contents SI Unit Example
frame_ID Reference frame identifier - must be different from all skew identifiers.

(Integer, maximum 10 digits)

frame_title Reference frame title

(Character, maximum 100 characters)

node_ID1 Node identifier N1

(Integer)

node_ID2 Node identifier N2

(Integer)

node_ID3 Node identifier N3

(Integer)

1. Let a moving reference frame ${\Lambda }_{t}\left(A,u,v,w\right)$ .
2. For each time t, the frame position and orientation are determined via its original position ${x}_{A}$ and a rotation (orientation) matrix $R$ .
3. Let $w$ be the instantaneous rotational velocity of $\lambda$ .
4. For each time t, the local coordinates of ${x}_{l}$ a point M with respect to the frame are related to its coordinates ${x}_{G}$ into the global system, as:(1)
${x}_{G}={x}_{A}+R{x}_{l}$
5. The relative displacement ${u}_{l}={x}_{l}-{x}_{l}^{0}$ of M between time 0 and t, with respect to the frame is related to its displacement with regard to the global system, as:(2)
${u}_{G}={u}_{A}+\left(R-{R}^{0}\right){x}_{l}+R{u}_{l}$
6. The relative velocity of M with respect to the frame is related to its velocity with regard to the global system, as:(3)
$R{v}_{l}={v}_{G}-{v}_{e}$

Where, ${v}_{e}={v}_{A}+\omega ×AM$ is the driving velocity; that is the velocity of the point coincident with M at time t and fixed with respect to the reference frame.

7. The relative acceleration of M with respect to the frame M is related to its acceleration with regard to the global system, as:
(4)
$R{\gamma }_{l}={\gamma }_{G}-{\gamma }_{e}-{\gamma }_{c}$
Where,
${\gamma }_{e}={\gamma }_{A}+d\omega }{dt}×AM+\omega ×\left(\omega ×AM\right)$
Driving acceleration
${\gamma }_{c}=2\omega ×{v}_{relative}$
Acceleration, due to Coriolis forces
8. For a moving reference frame, the reference frame position and orientation vary with time and are defined by N1, N2 and N3.

The origin of the frame is defined by the position of N1.

node_ID1and node_ID2 define ${Z}^{\prime }$

node_ID1 and node_ID3 define $X"$ (5)
$Y\text{'}={Z}^{\prime }\Lambda X"$
(6)
$X\text{'}=Y\text{'}\Lambda Z\text{'}$

Reference frame identifier must be different from all skew identifiers.