Editing Tilde (section)

===Physics===
Often in [[physics]], one can consider an [[equilibrium solution]] to an equation, and then a perturbation to that equilibrium. For the variables in the original equation (for instance <math>X</math>) a substitution <math>X\to x+\tilde{x}</math> can be made, where <math>x</math> is the equilibrium part and <math>\tilde{x}</math> is the perturbed part.

A tilde is also used in [[particle physics]] to denote the hypothetical [[supersymmetric]] partner. For example, an [[electron]] is referred to by the letter ''e'', and its [[superpartner]] the [[selectron (particle)|selectron]] is written ''ẽ''.

In multibody mechanics, the tilde operator maps three-dimensional vectors <math>\boldsymbol{\omega}\in\mathbb{R}^3</math> to skew-symmetrical matrices <math>\tilde{\boldsymbol{\omega}}=\begin{bmatrix}0&-\omega_3& \omega_2\\ \omega_3& 0& -\omega_1\\ -\omega_2&\omega_1&0\end{bmatrix}</math> (see <ref>{{cite journal |last1=Wallrapp |title=Standardization of flexible body modeling in multibody system codes, Part I: Definition of Standard Input Data |date=1994 |volume=22 |issue=3 |pages=283–304 |doi=10.1080/08905459408905214 |journal=Mechanics of Structures and Machines}}</ref> or <ref>{{cite journal |last1=Valembois |first1=R. E. |last2=Fisette |first2=P. |last3=Samin |first3=J. C. |title=Comparison of Various Techniques for Modelling Flexible Beams in Multibody Dynamics |journal=Nonlinear Dynamics |date=1997 |volume=12 |issue=4 |pages=367–397 |doi=10.1023/A:1008204330035|bibcode=1997NonDy..12..367V |s2cid=122487067 }}</ref>).