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. 2014 Feb 28;9(2):e77190. doi: 10.1371/journal.pone.0077190

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© 2014 Allison et al

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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By introducing non-conservative, or dissipative, elements into a system we need to generalise our concept of potential. The Lagrangian for this system can be written as . The additional term differs from the terms for the un-damped system in two key ways: the term is complex has an imaginary phase, of +j, and there is a fractional derivative of the coordinate, x ^(1/2).

Inline graphic — By introducing non-conservative, or dissipative, elements into a system we need to generalise our concept of potential. The Lagrangian for this system can be written as . The additional term differs from the terms for the un-damped system in two key ways: the term is complex has an imaginary phase, of +j, and there is a fractional derivative of the coordinate, x ^(1/2).