eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences April 2018 30 4 40 48 http://dx.doi.org/10.22147/jusps-B/300401 1464 article MINGLIANG ZHENG (zhmlwxcstu@163.com) 1 School of mechanical engineering, Zhejiang Sci-Tech University, Hangzhou, Zhengjiang, 310018, (China) <p style="text-align:justify">The constraint mechanical systems with quasi coordinates are more universal than generalized coordinates, in this paper, we study the Noether symmetries and conserved quantities of nonconservative singular systems in phase space. Firstly, the internal constraints induced by singularity are equivalent considered as extrinsic nonholonomic constraints, the canonical equations of constrained Hamilton systems with quasi coordinates are obtained by using transform to the Euler-Lagrange equations. Secondly, the infinitesimal transformations of time, quasi coordinates and generalized momentum are introduced, the definition, criterion and Noether theorem are obtained according to the regular action quantity keep generalized quasi invariance under the transformation, meanwhile, the inverse problem of the Noehter symmetry is also studied. Finally, an example is given to illustrate the application of the content. The results found that the rational use of quasi coordinates will make the constraints caused by the singularity of the system do not affect the standard form of the regular equations and avoid the emergence of constrained multipliers, the conservation is more concise.</p> https://ultraphysicalsciences.org/paper/1464/ Quasi coordinates constrained Hamilton systems Noether symmetries conserved quantities