/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)

 

Comments

  1. Let a moving reference frame Λ t ( A,u,v,w ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeu4MdW0aaS baaSqaaiaadshaaeqaaOWaaeWaaeaacaWGbbGaaiilaiaahwhacaGG SaGaaCODaiaacYcacaWH3baacaGLOaGaayzkaaaaaa@3FF7@ .
  2. For each time t, the frame position and orientation are determined via its original position x A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGbbaabeaaaaa@37E6@ and a rotation (orientation) matrix R MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCOuaaaa@36D1@ .
  3. Let w MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaC4Daaaa@36F7@ be the instantaneous rotational velocity of λ .
  4. For each time t, the local coordinates of x l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEamaaBa aaleaacaWGSbaabeaaaaa@3815@ a point M with respect to the frame are related to its coordinates x G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEamaaBa aaleaacaWGhbaabeaaaaa@37F0@ into the global system, as:(1)
    x G = x A + R x l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCiEamaaBa aaleaacaWGhbaabeaakiabg2da9iaahIhadaWgaaWcbaGaamyqaaqa baGccqGHRaWkcaWHsbGaaCiEamaaBaaaleaacaWGSbaabeaaaaa@3ED8@
  5. The relative displacement u l = x l x l 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCyDamaaBa aaleaacaWGSbaabeaakiabg2da9iaahIhadaWgaaWcbaGaamiBaaqa baGccqGHsislcaWH4bWaa0baaSqaaiaadYgaaeaacaaIWaaaaaaa@3F10@ 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 +( R R 0 ) x l +R u l MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCyDamaaBa aaleaacaWGhbaabeaakiabg2da9iaahwhadaWgaaWcbaGaamyqaaqa baGccqGHRaWkdaqadaqaaiaahkfacqGHsislcaWHsbWaaWbaaSqabe aacaaIWaaaaaGccaGLOaGaayzkaaGaaCiEamaaBaaaleaacaWGSbaa beaakiabgUcaRiaahkfacaWH1bWaaSbaaSqaaiaadYgaaeqaaaaa@46F6@
  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 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCOuaiaahA hadaWgaaWcbaGaamiBaaqabaGccqGH9aqpcaWH2bWaaSbaaSqaaiaa dEeaaeqaaOGaeyOeI0IaaCODamaaBaaaleaacaWGLbaabeaaaaa@3F01@

    Where, v e = v A +ω×AM MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCODamaaBa aaleaacaWGLbaabeaakiabg2da9iaahAhadaWgaaWcbaGaamyqaaqa baGccqGHRaWkcaWHjpGaey41aqRaaCyqaiaah2eaaaa@4105@ 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 γ l = γ G γ e γ c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaCOuaiaaho 7adaWgaaWcbaGaamiBaaqabaGccqGH9aqpcaWHZoWaaSbaaSqaaiaa dEeaaeqaaOGaeyOeI0IaaC4SdmaaBaaaleaacaWGLbaabeaakiabgk HiTiaaho7adaWgaaWcbaGaam4yaaqabaaaaa@430B@
    Where,
    γ e = γ A + d ω d t × A M + ω × ( ω × A M ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaC4SdmaaBa aaleaacaWGLbaabeaakiabg2da9iaaho7adaWgaaWcbaGaamyqaaqa baGccqGHRaWkdaWccaqaaiaadsgacaWHjpaabaGaamizaiaadshaaa Gaey41aqRaaCyqaiaah2eacqGHRaWkcaWHjpGaey41aq7aaeWaaeaa caWHjpGaey41aqRaaCyqaiaah2eaaiaawIcacaGLPaaaaaa@4F45@
    Driving acceleration
    γ c = 2 ω × v r e l a t i v e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaC4SdmaaBa aaleaacaWGJbaabeaakiabg2da9iaaikdacaWHjpGaey41aqRaaCOD amaaBaaaleaacaWGYbGaamyzaiaadYgacaWGHbGaamiDaiaadMgaca WG2bGaamyzaaqabaaaaa@4631@
    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 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GabCOwayaafaaaaa@3AC5@

    node_ID1 and node_ID3 define X" MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaCiwaiaackcaaaa@3B5D@ (5)
    Y ' = Z Λ X " MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaCywaiaacEcacqGH9aqpceWHAbGbauaacqqHBoatcaWHybGaaiOi aaaa@4054@
    (6)
    X ' = Y ' Λ Z ' MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8akY=xipgYlh9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaCiwaiaacEcacqGH9aqpcaWHzbGaai4jaiabfU5amjaahQfacaGG Naaaaa@40F8@

    starter_frame_move2D
    Figure 1.

    Reference frame identifier must be different from all skew identifiers.