Conformal invariance and conserved quantity of Mei symmetry for higher-order nonholonomic system

Nonlinear Control of a Robot Manipulator with a Nonholonomic Jerk Constraint

“…Such constraints are classified as program constraints that arise by imposition of certain design conditions on the allowable motions. New forms of the differential equations of systems with higher‐order nonholonomic constraints (HONCs) have been derived by a number of authors . Tracking control problems for such systems have been studied in .…”

Conformal Invariance and Conserved Quantity of Mei Symmetry for Appell Equations in a Holonomic System with Mass Variable

“…Galiullin et al had proposed concepts of conformal invariance and conformal factor of Birkhoff equations in the study of dynamics in Birkhoffian systems [11], and discussed the relationships between the invariance and the conformal invariance, Lie symmetry and the conformal invariance under the infinitesimal transformations of Pfaff action in 1997. Chinese scholars have carried out certain new researches and have obtained achievements in the study of symmetries and conserved quantities for mechanical systems by means of the theories of the conformal invariance [12][13][14][15][16][17][18][19] from the beginning of the twenty-first century till now. However, fewer results to Appell equations is gained for a long time, at present, there is no papers to present publicly about conformal invariance and conserved quantity of Mei symmetry of Appell equations expressed directly from Appell functions in a holonomic system with variable mass.…”

Conformal invariance and conserved quantity of Mei symmetry for Appell equations in a nonholonomic system of Chetaev’s type

“…In 1997, Galiullin et al had proposed concepts of conformal invariance and conformal factor of Birkhoff equations in the study of dynamics in Birkhoffian systems [23], and discussed the relationships between the invariance and the conformal invariance, Lie symmetry and the conformal invariance under the infinitesimal transformations of Pfaff action. Since entering the twenty-first century, Chinese scholars have carried out certain new researches and have gained some achievements in the study of symmetries and conserved quantities for mechanical systems by means of theories of the conformal invariance [24][25][26][27][28][29][30][31][32][33][34][35]. However, for a long time, there are fewer results to Appell equations.…”