9.2 Lagrange's Principle in Terms of Quasi-Coordinates
9.2.1 Lagrange's Principle
9.2.2 Deduction of Equations of Motion in Terms of Quasi-Coordinates by Means of Lagrange's Principle
9.3 Remarks

l0 Integral Variational Principles for Nonholonomic Systems
10.1 Definitions of Variation
10.1.1 Necessity of Definition of Variation of Generalized Velocities for Nonholonomic Systems
10.1.2 Suslov's Definition
10.1.3 HSlder's Definition
10.2 Integral Variational Principles in Terms of Generalized Coordinates for Nonholonomic Systems
10.2.1 Hamilton's Principle for Nonholonomic Systems
10.2.2 Necessary and Sufficient Condition Under Which Hamilton's Principle for Nonholonomic Systems Is Principle of Stationary Action
10.2.3 Deduction of Equations of Motion for Nonholonomie Systems by Means of Hamilton's Principle
10.2.4 General Form of Hamilton's Principle for Nonhononomic Systems
10.2.5 Lagranges Principle in Terms of Generalized Coordinates for Nonholonomic Systems
10.3 Integral Variational Principle in Terms of QuasiCoordinates for Nonholonomic Systems
10.3.1 Hamilton's Principle in Terms of Quasi-Coordinates
10.3.2 Lagrange's Principle in Terms of Quasi-Coordinates
10.4 Remarks

11 Pfaff-Birkhoff Principle
11.1 Statement of Pfaff-Birkhoff Principle
11.2 Hamilton's Principle as a Particular Case of Pfaff-Birkhoff Principle
11.3 Birkhoff's Equations
11.4 Pfaff-Birkhoff-d'Alembert Principle
11.5 Remarks

III Differential Equations of Motion of Constrained Mechanical
Systems

12 Lagrange Equations of Holonomic Systems
12.1 Lagrange Equations of Second Kind
12.2 Lagrange Equations of Systems with Redundant Coordinates
12.3 Lagrange Equations in Terms of Quasi-Coordinates
12.4 Lagrange Equations with Dissipative Function
12.5 Remarks

13 Lagrange Equations with Multiplier for Nonholonomic Systems
13.1 Deduction of Lagrange Equations with Multiplier
13.2 Determination of Nonholonomic Constraint Forces
13.3 Remarks

14 Mac Millan Equations for Nonholonomie Systems
14.1 Deduction of Mac Millan Equations
14.2 Application of Mac MiUan Equations
14.3 Remarks

15 Volterra Equations for Nonholonomic Systems
15.1 Deduction of Generalized Volterra Equations
15.2 Volterra Equations and Their Equivalent Forms
15.2.1 Volterra Equations of First Form
15.2.2 Volterra Equations of Second Form
15.2.3 Volterra Equations of Third Form
15.2.4 Volterra Equations of Fourth Form
15.3 Application of Volterra Equations
15.4 Remarks

16 Chaplygin Equations for Nonholonomic Systems
16.1 Generalized Chaplygin Equations
16.2 Voronetz Equations
16.3 Chaplygin Equations
16.4 Chaplygin Equations in Terms of Quasi-Coordinates
16.5 Application of Chaplygin Equations
16.6 Remarks
……


Ⅳ Special Problems in Constrained Mechanical Systems
Ⅴ Integration Methods in Constrained Mechanical Systems
Ⅵ Symmetries and Conserved Quantities in Constrained Mechanical Systems

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