.. _other_damping: Damping force ============= Linear damping -------------- The linear damping force, applied on a body, can be expressed using generalized notations: .. math::  \mathbf{f}_{LD} = \mathbf{M}_{LD} \mathcal{V} where :math:\mathcal{V} = \begin{bmatrix} \mathbf{u} \\ \mathbf{\omega} \end{bmatrix} is the generalized velocity of the body and :math:\mathbf{M}_{LD} is the damping matrix. The velocity of the body can be taken relatively to a fluid flow velocity (air or water). Quadratic damping ----------------- The quadratic damping force is only applied on the translational velocity of a body, and therefor cannot be given using generalized notations: .. math:: \mathbf{f}_{QD} = -\frac{1}{2} \rho_{fluid} \begin{bmatrix} C_x S_x |u_x| u_x \\C_y S_y |u_y| u_y \\C_z S_z |u_z| u_z \\ \end{bmatrix} where - :math:\rho_{fluid} is the fluid density. - :math:C_i are the damping coefficients, - :math:S_i are the projected surfaces, - :math:\mathbf{u} = \begin{bmatrix}u_x & u_y & u_z \end{bmatrix} is the body velocity. It can also be taken relatively to a fluid flow velocity, but be careful not to use a :any:current load which might be redundant.