- See also
- References
A free motion equation is a differential equation that describes a mechanical system in the absence of external forces, but in the presence only of an inertial force depending on the choice of a reference frame.
In non-autonomous mechanics on a configuration space 
, a free motion equation is defined as a second order non-autonomous dynamic equation on which is brought into the form
with respect to some reference frame 
on . Given an arbitrary reference frame 
on , a free motion equation reads
where 
is a connection on associates with the initial reference frame . The right-hand side of this equation is treated as an inertial force.
A free motion equation need not exist in general. It can be defined if and only if a configuration bundle
of a mechanical system is a toroidal cylinder 
.
See also
- Non-autonomous mechanics
- Non-autonomous system (mathematics)
- Analytical mechanics
- Fictitious force
References
- De Leon, M., Rodrigues, P., Methods of Differential Geometry in Analytical Mechanics (North Holland, 1989).
- Giachetta, G., Mangiarotti, L., Sardanashvily, G., Geometric Formulation of Classical and Quantum Mechanics (World Scientific, 2010) {{ISBN|981-4313-72-6}} (arXiv: 0911.0411).
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