RIGIDBODY

The geometry with MOVE-flag $MOVE_index$ moves due to the acting forces of the flow as well as additional outer forces and momentum. In particular, we solve the ODE of movement of rigid rotating bodies: \begin{align} \frac{d }{dt} \left( \mathbf{x}_{COG} \right) = \mathbf{v}_{COG}\end{align} \begin{align} \frac{d }{dt} \left( m \cdot \mathbf{v}_{COG} \right) = F_{fluid} + F_{gravity} + F_{outer} + \left( F_{contact} + F_{friction} \right)\end{align} \begin{align} \frac{d}{dt} \left( \mathbf{I} \cdot \mathbf{\omega}_{COG} \right) = M_{fluid} + M_{outer} + \left( M_{contact} + M_{friction} \right)\end{align} The variables are

• \( t\) : time
• \( m\) : mass of the body,
• \( \mathbf{x}_{COG}\) : position of the center of gravity of the body ; this can be interrogated by the function xCOG() ,
• \( \mathbf{v}_{COG}\) : velocity of the center of gravity; this can be interrogated by the function vCOG() ,
• \( F_{fluid}\) : forces acting from the fluid onto the body (automatically measured and applied!!!), to be requested by the function FCOG() ,
• \( F_{gravity}\): the gravity forces deduced from the definition of gravity of the appropriate material ,
• \( F_{outer}\) : additional / outer forces other than fluid or gravity / body forces ,
• \( \mathbf{I}\) : tensor of rotational inertia ,
• \( \mathbf{\omega}_{COG}\) : rotational speed about the center of gravity of the body, to be requested by the function omCOG() ,
• \( M_{fluid}\) : moment about the center of gravity (automatically measured and applied!!!!), this can be inquired by the function MCOG() ,
• \( M_{outer}\) : outer moments other than the moment applied by the fluid ,
• \( F_{contact}, M_{contact}\) : if RIGIDBODY_UseCollisionModel > 0 , then MESHFREE detects the body-body- and body-boundary-intersections and automatically applies contact forces and moments \( M_{contact} = \left( \mathbf{x}_{contact} - \mathbf{x}_{COG} \right) \times F_{contact}\) .

Remark: the items above have to be initialized in the MOVE statement (see below)

• (xCenterInit, yCenterInit, zCenterInit): initial center of gravity \( \mathbf{x}_{COG}\)
• Mass: mass of RIGIDBODY \( m\)
• (xxInertia, xyInertia, xzInertia, yxInertia, yyInertia, yzInertia, zxInertia, zyInertia, zzInertia): initial tensor of inertia \( \mathbf{I}\)
• (xVelocityInit, yVelocityInit, zVelocityInit): initial velocity \( \mathbf{v}_{COG}\)
• (xOmegaInit, yOmegaInit, zOmegaInit): inital rotational state \( \mathbf{\omega}_{COG}\)
• (xForce, yForce, zForce): outer forces \( F_{outer}\)
• (xMomentum, yMomentum, zMomentum): outer momentum \( M_{outer}\)
• %RIGIDBODY_FixVelocity% , v_x, v_y, v_z, : fix a velocity vector (that is fix a velocity in a given direction). The direction of fixation is \( \frac{1}{\| (v_x,v_y,v_z) \|)} \left(v_x,v_y,v_z \right)\) the speed to fix is \( \| \left(v_x,v_y,v_z \right) \|)\) . So, it becomes clear, that 0 velocity cannot be fixed, in this case a tiny value has to be given. Be aware, that you can provide up to three %RIGIDBODY_FixVelocity% statements
• %RIGIDBODY_FixOmega% , omega_x, omega_y, omega_z : fix a rotational speed vector (that is fix the speed around a given axis). The direction of axis is \( \frac{1}{\| (\omega_x,\omega_y,\omega_z) \|)} \left(\omega_x,\omega_y,\omega_z \right)\) the speed to fix is \( \| \left(\omega_x,\omega_y,\omega_z \right) \|)\) . So, it becomes clear, that 0 rotational speed cannot be fixed, in this case a tiny value has to be given. Be aware, that you can provide up to three %RIGIDBODY_FixOmega% statements