System of ordinary differential equations of translational and angular ship motion. More...

Public Types
using	value_type = T

using	vec2 = blitz::TinyVector< T, 2 >

using	vec3 = blitz::TinyVector< T, 3 >

using	ship_type = Ship< T >

using	panel_type = Ship_hull_panel< T, 3 >

using	panel_array = std::vector< panel_type >

using	state_vector_type = typename ship_type::state_vector_type

using	variables_type = typename ship_type::variables_type

using	basis_type = typename ship_type::basis_type

using	rotation_matrix_type = typename ship_type::rotation_matrix_type

using	quaternion_type = typename ship_type::quaternion_type

using	waterline_type = vtb::geometry::Polyline< T, 3 >

Public Member Functions
	Ship_motion_equation (const rotation_matrix_type &inertia_matrix)

void	solve (T t, const state_vector_type &v, state_vector_type &dv)

variables_type	operator() (T t, const variables_type &vars)

state_vector_type	operator() (T t, const state_vector_type &vars)

const rotation_matrix_type &	inertia_matrix () const

void	inertia_matrix (const rotation_matrix_type &rhs)

void	gravity_force (const vec3 &rhs)

void	total_force (const vec3 &rhs)

void	total_torque (const vec3 &rhs)

void	damping (const vec3 &rhs)

const vec3 &	damping () const

T	displacement () const

const vec3 &	total_force () const

const vec3 &	total_torque () const

const vec3 &	centre_of_gravity () const

const vec3 &	centre_of_buoyancy () const

const vec3 &	centre_of_floatation () const

const vec3 &	centre_of_wind () const

void	calc_forces_and_torques (const ship_type &ship, const panel_array &wetted_panels, const panel_array &dry_panels, const waterline_type &waterline)

void	clear ()

Detailed Description

System of ordinary differential equations of translational and angular ship motion.

Uses Earth-fixed coordinate system.
Every term in the equation is divided by ship mass.
Uses the formulae adapted from [baraff1997rigid:]
\[ \frac{d}{dt}\left[ \begin{array}{c} \vec{x}(t)\\ q(t)\\ \vec{P}(t)\\ \vec{L}(t) \end{array} \right] = \left[ \begin{array}{c} \vec{v}(t)\\ \frac{1}{2}\vec\omega(t)q(t)\\ \vec{F}(t)\\ \vec\tau(t) \end{array} \right]. \]
Here \(\vec{x}\) is ship position, \(q\) is ship orientation in quaternion form, \(\vec{P}\) is linear momentum, \(\vec{L}\) is angular momentum, \(\vec{F}\) is a vector of external forces, \(\vec\tau\) is a vector of external force moments, \(\vec\omega\) is angular velocity. Formulae for auxiliary physical quantities:
\[ \vec{P}(t) = m\vec{v}(t) \qquad \vec{L}(t) = I(t)\vec\omega(t) \qquad I(t) = R(q(t)) \, I_{\text{body}} \, R(q(t))^{T} \]
Froude—Krylov, gravity and wind force moments are computed with respect to centre of floatation (see [megel2010metacentre]).

Definition at line 59 of file ship_motion_solver.hh.

Public Types