Nielsen form

Lagrange's Equations in Lagrangian mechanics are usually written in the form:$\{mathrm\{d\}\; over\; mathrm\{d\}t\}\{partial\{T\}over\; partial\{q\text{'}\_j-\{partial\{T\}over\; partial\; q\_j\}\; =\; Q\_j$

The "Nielsen Form" is an alternative formulation written as:$\{partial\{T\text{'}\}over\; partial\{q\text{'}\_j-2\{partial\{T\}over\; partial\; q\_j\}\; =\; Q\_j$

These two forms are equivalent; this can easily be shown by the Chain rule. Notice that if

:$T\; =\; T(q\_i,\; q\text{'}\_i)$

then

:as desired.