# /FRAME/MOV

Block Format Keyword Describes moving frames. Relative motion with respect to a reference frame.

## Format

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

## Definitions

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)

Dir
X, Y, or Z
Define the local direction of N1 N2 axis

Default = X (Text)

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 $\text{Λ}$ .
4. For each time t, the local coordinates ${x}_{l}$ of 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, ${\gamma }_{e}={\gamma }_{A}+d\omega }{dt}×AM+\omega ×\left(\omega ×AM\right)$ is the driving acceleration and ${\gamma }_{c}=2\omega ×{v}_{relative}$ is the 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 axis definition depends on the input for Dir.
• When Dir=X

node_ID1 amd node_ID2 define $X\text{'}$

node_ID1 and node_ID3 define $Y"$
• $Z\text{'}=X\text{'}\Lambda Y"$
• $Y\text{'}={Z}^{\prime }\Lambda {X}^{\prime }$
• When Dir=Y

node_ID1 and node_ID2 define $Y\text{'}$

node_ID1 and node_ID3 define $Z"$
• $X\text{'}={Z}^{″}\Lambda {Y}^{\prime }$
• $Z\text{'}={X}^{\prime }\Lambda {Y}^{\prime }$
• Case Dir=Z

node_ID1 and node_ID2 define $Z\text{'}$

node_ID1 and node_ID3 define $X"$
• ${Y}^{\prime }={X}^{″}\Lambda {Z}^{\prime }$
• ${X}^{\prime }={Y}^{\prime }\Lambda {Z}^{\prime }$
The skew is defined by $X\text{'}$ , $Y\text{'}$ and $Z\text{'}$
9. In a 2D analysis N1 and N2 define $Y\text{'}$ .
10. Reference frame identifier must be different from all skew identifiers.