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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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We consider the simple introductory problem of a mass, m, on a spring, with stiffness constant of k. The kinetic energy stored by the inertia of the mass is denoted by . The elastic potential energy stored in the spring is denoted by . The independent coordinate is denoted by the position, x. The Lagrangian function is traditionally written as , which can be written explicitly as .

Inline graphic — We consider the simple introductory problem of a mass, m, on a spring, with stiffness constant of k. The kinetic energy stored by the inertia of the mass is denoted by . The elastic potential energy stored in the spring is denoted by . The independent coordinate is denoted by the position, x. The Lagrangian function is traditionally written as , which can be written explicitly as .