Node GravityNode#

Defined in mime.nodes.body._gravity.GravityNode.

Algorithm MIME-NODE-113.

Weight and buoyancy on a body in a medium at rest: the wrench about the centre of mass, with the buoyancy’s couple where the centre of buoyancy is off it.

Governing equations#

\[ \mathbf{F} = m \, \mathbf{g} - \rho_{f} V \, \mathbf{g}, \quad \boldsymbol{\tau} = R(\mathbf{q}) \, \mathbf{c}_{b} \times \left( -\rho_{f} V \, \mathbf{g} \right) \]

Discretisation#

none declared; a node whose order depends on its construction declares it with the discretization_order() hook, which is read from a built node.

Assumptions#

  • The medium is at rest and its density uniform: a flow that carries its own hydrostatic load would count the buoyancy twice

  • The weight acts at the centre of mass and the buoyancy at the centre of buoyancy, both fixed in the body

Limitations#

none declared

Declared regimes (not evidenced here)#

none declared

References#

[@TatumClassicalMechanics]

Symbols#

Symbol

Kind

Name

Units

Implemented by

\(\mathbf{F}\)

state

wrench

N; N m

mime.nodes.body._gravity.GravityNode.wrench

\(\boldsymbol{\tau}\)

state

wrench

N; N m

mime.nodes.body._gravity.GravityNode.wrench

\(m\)

parameter

mass

kg

mime.nodes.body._gravity.GravityNode.wrench

\(\mathbf{g}\)

parameter

gravity

m/s^2

mime.nodes.body._gravity.GravityNode.wrench

\(\rho_{f}\)

parameter

fluid_density

kg/m^3

mime.nodes.body._gravity.GravityNode.wrench

\(V\)

parameter

buoyant_volume

m^3

mime.nodes.body._gravity.GravityNode.wrench

\(\mathbf{c}_{b}\)

parameter

centre_of_buoyancy

m

mime.nodes.body._gravity.GravityNode.wrench

Built by#