Table 4. Table of mechanical Lagrangian terms.

parameter	Lagrangian 3D	Lagrangian 1D	order, k	Euler-Lagrange
mass, m			1	−mx (2)
damping, c			1/2	−cx (1)
spring, k			0	−kx (0)

Lagrangian terms for mechanical parameters: We list the common lumped mechanical parameters. From left to right, we list the common symbol for the parameter, the Lagrangian for the 3D vector case (in terms of position or momentum), the Lagrangian for the 1D case (in terms of the position only), the order of differentiation employed, and the resulting them in the Euler-Lagrange Equation. We use the sign convention of Gel'fand and Fomin [16] for the terms of the Euler-Lagrange Equation. Some authors introduce an additional minus sign, in order to make all of these terms positive.