Node MagneticForceNode#

Defined in mime.nodes.magnetic._force.MagneticForceNode.

Algorithm MIME-NODE-107.

The force of a field’s gradient on a body’s permanent moment, F = G^T m, and its torque about the centre of mass where the magnet sits off it.

Governing equations#

\[ \mathbf{F} = \mathbf{G}^{\top} \mathbf{m}, \quad \boldsymbol{\tau} = \mathbf{l} \times \mathbf{F}, \quad \mathbf{m} = R(\mathbf{q}) \, \mathbf{m}_{b}, \quad \mathbf{l} = R(\mathbf{q}) \, \mathbf{c}_{b} \]

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#

  • A point dipole in a current-free field, the gradient read at the body’s centre of mass

  • A rigid, permanent moment

Limitations#

none declared

Declared regimes (not evidenced here)#

none declared

References#

[@Jackson1998]

Symbols#

Symbol

Kind

Name

Units

Implemented by

\(\mathbf{F}\)

state

wrench

N; N m

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\(\boldsymbol{\tau}\)

state

wrench

N; N m

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\(\mathbf{G}\)

input

gradient

T/m

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

parameter

moment

A m^2

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\(\mathbf{q}\)

input

pose

m; 1

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

parameter

magnet_centre

m

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Built by#