Editing Nonholonomic system (section)

==History==
[[Norman Macleod Ferrers|N. M. Ferrers]] first suggested to extend the equations of motion with nonholonomic constraints in 1871.<ref name="Ferrers1872">{{cite journal|last=Ferrers|first=N.M.|title=Extension of Lagrange's equations|journal=Q. J. Pure Appl. Math.|volume=XII|year=1872|pages=1&ndash;5}}</ref>
He introduced the expressions for Cartesian velocities in terms of generalized velocities.
In 1877, E. Routh wrote the equations with the Lagrange multipliers. In the third edition of his book<ref name="Routh1884">{{cite book |last=Routh |first=E. |date=1884 |title=Advanced part of a Treatise on the Dynamics of a System of Rigid Bodies |url=https://archive.org/details/advancedpartatr03routgoog |location=London }}</ref>  for linear non-holonomic constraints of rigid bodies, he introduced the form with multipliers, which is now called the Lagrange equations of the second kind with multipliers. The terms the holonomic and nonholonomic systems were introduced by Heinrich Hertz in 1894.<ref name="Hertz1894">{{cite book |last=Hertz |first=H. |date=1894 |title=ie Prinzipien derMechanik in neuem Zusammenhange dargestellt }}</ref>
In 1897, S. A. Chaplygin first suggested to form the equations of motion without Lagrange multipliers.<ref name="Chaplygin1897">{{cite journal|last=Chaplygin|first=S.A. |date=1897 |title=О движении тяжелого тела вращения по горизонтальнойплоскости |trans-title=A motion of heavy body of revolution on a horizontal plane |language=ru |journal=антpопологии и этногpафии |publisher=отделения физических наук общества любителей естествознания |page=10&ndash;16 |volume=1|issue=IX }}</ref>
Under certain linear constraints, he introduced on the left-hand side of the equations of motion a group of extra terms of the Lagrange-operator type.
The remaining extra terms characterise the nonholonomicity of system and they become zero when the given constrains are integrable.
In 1901 P. V.Voronets generalised Chaplygin's work to the cases of noncyclic holonomic coordinates 
and of nonstationary constraints.<ref name="Voronets1901">{{cite journal|last=Voronets|first=P. |date=1901 |title=Об уравнениях движения для неголономных систем |trans-title=Equations of motion of nonholonomic systems |language=ru |journal=Матем. Сб. |page=659&ndash;686 |volume=4 |issue=22}}</ref>