Analytical mechanics deals mainly with systems of bodies subject to ideal constraints, providing study methods distinct to the classical ones, based on which equilibrium and motion equations, respectively, can be directly determined, without the need to isolate first the bodies and replace the constraints with reactions.

Chapter 1. Introductive notions

1.1. Generalities

1.2. Constraints

1.3. Generalized coordinates

1.4. Displacements

Chapter 2. Principle of virtual work

2.1. Generalities

2.2. The first form of the principle of virtual work

2.3. The second form of the principle of virtual work in the case of a system of

material points acted by arbitrary forces

2.4. The second form of the principle of virtual work in the case of a system of

material points acted by conservative forces

2.5. Torricelli’s principle

2.6. Principle of virtual power

Chapter 3. D’Alembert’s principle

3.1. Generalities

3.2. D’Alembert’s principle for a material point

3.3. D’Alembert’s principle for a system of material points

3.4. Reduction elements of the inertia forces with respect to a point

3.5. Reduction elements of the inertia forces with respect to the center of mass

3.6. D’Alembert’s principle for a rigid body

3.7. Calculation of the reduction elements of the inertia forces acting upon a

rigid

Cuprins:

Chapter 4. Lagrange’s equations

4.1. Generalities

4.2. D’Alembert-Lagrange equation

4.3. Lagrange’s equations of the first kind

4.4. Lagrange’s equations of the second kind in the case of arbitrary forces

4.5. Lagrange’s equations of the second kind in the case of conservative forces

Chapter 5. Lagrange’s equations for systems with dependent variables

5.1. Generalities

5.2. Case of holonomic systems with dependent variables

5.3. Case of non-holonomic systems with linear velocity constraints

Chapter 6. Hamilton’s canonical equations

6.1. Generalities

6.2. Generalized momenta

6.3. Hamilton function

6.4. Hamilton’s canonical equations

6.5. Hamilton’s canonical equations in the case of a system acted by conservative forces

References