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Newton Mechanics
1. Kinematics
1.1. Point
1.2. Rigid Body
1.3. Continuous Medium
1.4. Relative Kinematics
1.5. Rotations
1.5.1. Tensor formalism for rotations
1.5.2. Rotation parametrization: axis and angle
1.5.3. Rotation parametrization: Euler’s angles
1.5.4. Rotation parametrization: quaternions
2. Actions
2.1. Force, Moment of a Force, Distributed Actions
2.2. Work and Power
2.3. Conservative Actions
2.4. Examples of Forces
2.5. Constraint Reactions
3. Inertia
4. Dynamics
4.1. Principles of Newtonian Mechanics
4.2. Equations of Motion and Conservation Principles
4.3. Equations of motion of a point mass
4.4. Equations of motion of a discrete system of point masses
4.5. Equations of motion of a rigid body
4.6. Equations of motion for continuous media
4.7. Particular Motions
4.8. Equilibrium and Stability
Analytical Mechanics
5. Lagrangian Mechanics
5.1. Lagrange Equations of the Second Kind
5.1.1. Point
5.1.2. System of points
5.1.3. Rigid Body
5.2. Lagrange Equations of the First Kind
5.3. Lagrangian functions and time dependence
5.3.1. Lagrangian function with no explicit dependence on time
5.3.2. Lagrangian function with explicit dependence on time
5.4. Constraints classification
5.5. Properties of the Lagrangian approach to classical mechanics
6. Hamiltonian Mechanics
Exercises
7. Dynamics
8. Gravitation
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Equations of motion for continuous media
4.6.
Equations of motion for continuous media
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