Part I STATICS
1. INTRODUCTION
1.1 Object and divisions of Classical Mechanics
1.2 Fundamental and derived notions
1.3 Theoretical models used in Mechanics
1.4 Fundamental Principles of Mechanics
1.5 Physical quantities. Units of measure
2. ELEMENTS OF ALGEBRA AND VECTOR ANALYSIS
2.1 Scalars and vectors properties
2.2 Grapho-analytical definitions of vectors
2.2.1 Projection of a vector on an axis
2.2.2 Projections on coordinate axes
2.2.3 Analytical expression of a vector
2.3 Basic operations with concurrent vectors
2.4 Vector multiplications
2.4.1 Multiply a vector with a scalar
2.4.2 Scalar product (dot product)
2.4.3 Vector product (cross product)
2.4.4 Mixed product
2.4.5 Double vector product
2.5 Basic operations in vector analysis
2.5.1 Derivative and differential of a vector function
2.5.2 Geometric interpretations
2.5.3 Derivative rules in vector operations
2.5.4 The integration of the vectorial functions
2.5.5 Vector integration rules
2.6 Matrix relationships between vectors
2.6.1 Generalities
2.6.2 Matrix expression of a vector
2.6.3 Vector operations in matrix form
3 REDUCTION OF FORCE SYSTEMS
3.1 Generalities on forces
3.1.1 Mechanical effect of force
3.1.2 Analytical definition of force
3.1.3 The moment of a force towards a point
3.1.4 The moment of a force towards an axis
3.1.5 Theorem of moments
3.1.6 Torque of forces
3.2 Reducing concurrent forces
3.2.1 Generalities
3.2.2 Graphic calculation
3.2.3 Analytical calculation
3.3 Reduction of any systems of force
3.3.1 Reducing a force to a point. Torsor
3.3.2 The torsor of a system of forces of any kind
3.3.3 Variation of the torsor when changing the calculation point. Invariants.
3.3.4 Minimal torsor. Central axis
3.3.5 Reducing cases
3.4 Reduction of particular force systems
3.4.1 Reduction of coplanar system of forces
3.4.2 Reduction of parallel forces
3.4.3 Reduction of distributed forces
4. CENTER OF MASS
4.1 Generalities
4.2 Mass center of a material points system
4.3 Mass center of a rigid solid body
4.4 Homogeneous bodies
4.4.1 Density
4.4.2 Position of the center of mass
4.4.3 Analytically defined bodies
4.4.4 Curves in plane
4.4.5 Curves in space
4.4.6 Surfaces in plane
4.4.7 Surfaces in space
4.4.8 Volumes
4.5 Composed bodies
4.6 Rotating bodies
4.7 Special methods of calculation
5. STATICS OF THE MATERIAL POINT
5.1 Generalities
5.2 Links of the material point
5.3 Analytically defined links
5.4 Links with friction
5.5 Echilibrium of material point
6. STATICS OF SOLID RIGID BODY
6.1 Generalities
6.2 Links of solid rigid body
6.3 Echilibrium of solid rigid body
6.4 Friction in the links of the rigid solid body
6.4.1 Sliding friction
6.4.2 Rolling friction
6.4.3 Pivoting friction
6.4.4 Friction in joints
6.4.5 Friction of wires
7. STATICS OF BODIES SYSTEMS
7.1 Generalities
7.2 Method of bodies isolation
7.3 Lattice beams
8. STATICS OF THE WIRES
8.1 Generalities
8.2 General equilibrium equations
8.3 Equilibrium equations in Cartesian coordinates
8.4 Equilibrium equations in the Frenet trihedral
8.5 Hyperbolic functions. General relationships
8.6 The general study of yhe homogeneous hard wire
8.7 Special problems in the Statics of wires
8.7.1 Very stretched wire
8.7.2 The wire with imposed lenght
8.7.3 Wire with fixed additional load
8.7.4 Wire with additional mobile load
Part II KINEMATICS
9. KINEMATICS OF THE MATERIAL POINT
9.1 Generalities
9.1.1 General kinematic parameters
9.1.2 Angular kinematic parameters
9.2 Kinematic parameters of movement in different coordinate systems
9.2.1 Cartesian coordinates
9.2.2 Polar coordinates
9.2.3 Cylindrical coordinates
9.2.4 Spherical coordinates
9.2.5 Intrinsic coordinates (Frenet)
9.3 Particular movements of the material point
9.3.1 Rectilinear movement
9.3.2 Circular motion
9.3.3 Uniform movement on circular helix
9.3.4 Harmonic oscillating motion
10. KINEMATIC OF THE RIGID SOLID BODY
10.1 Generalities
10.2 Kinematic parameters of rigid solid body movement
10.3 Simple particular movements of rigid solid body
10.3.1 Translation movement
10.3.2 Rotational movement
10.3.3 Helicoidal movement
10.4 Plan-parallel movement
10.4.1 General characteristics of movement
10.4.2 Special points in the plane of movement
10.4.3 Vector study of velocities and accelerations
10.4.4 Grapho-analytical methods
10.4.5 Analytical method
10.5 Movement of a body with a fixed point
11. COMPOSED MOVEMENTS
11.1 Generalities
11.2 Composed movements of the material point
11.2.1 Vector and matrix study of kinematic parameters
11.2.2 Analytical method
11.3 Composed movements of rigid solid body
11.3.1 Defining movements
11.3.2 Kinematic parameters in the general case
11.3.3 Angular parameters of absolute motion
11.4 Particular composed movements
11.4.1 Composed translations
11.4.2 Composed parallel rotation
11.4.3 Composed concurrent rotations
12. KINEMATICS OF BODY SYSTEMS
12.1 Generalities
12.2 Simple mechanical transmissions
12.3 Complex transmissions by wires
12.4 Simple common mechanisms
12.4.1 The crank-slider mechanism
12.4.2 The four-bar mechanism
12.4.3 Oscillating slider mechanism
12.4.4 Open kinematic chain mechanism
13. DYNAMIC ANALYSIS OF THE MATERIAL POINT
13.1 Generalities
13.1.1 Dynamic analysis objective
13.1.2 General dynamic parameters
13.1.3 The force function. Conservative forces
13.1.4 General theorems of Dynamics in the case of material point
13.2 Dynamics of the free material point
13.2.1 General equations of motion in different coordinate systems
13.2.2 Numerical integration of motion equations
13.2.3 Movement of heavy material point in a non-resistant environment
13.2.4 Movement of heavy material point in a resistant environment
13.2.5 The movement of the material point operated by a central force.
General case
13.2.6 The movement of the material point under the action of the
universal
force of attraction.
13.3 Dynamics of the material point with links
13.3.1 Equations of motion
13.3.2 Movement on the inclined plane
13.3.3 Spherical pendulum
13.3.4 Mathematical pendulum
13.3.5 The small oscillations of the mathematical pendulum
14. DYNAMIC OF THE OSCILLATORY MOVEMENT OF THE
MATERIAL POINT
14.1 Generalities
14.2 Free oscillations without damping
14.3 Free oscillations with damping
14.4 Forced oscillations without damping
14.5 Forced oscillations with damping
15. DINAMIC OF THE MATERIAL POINT'S COMPOSED MOVEMENTS
15.1 Generalities
15.2 General equation of relative motion
15.3 Movement of a slide on a rotating oblique bar
15.4 Movement of a particle on the inner surface of a inclined cylinder
16. MECHANICAL MOMENTS OF INERTIA
16.1 Generalities
16.2 Variation of inertia moments from parallel axes
16.3 Variation of moments of inertia from concurrent axes
16.4 Directions and main moments of inertia
16.5 Usual moments of inertia
16.5.1 General relations
16.5.2 Moments of inertia at homogeneous bar
16.5.3 Moments of inertia at homogeneous plates
16.5.4 Moments of inertia at homogeneous volumes
16.5.5 Special methods of calculation
17. DINAMIC OF THE RIGID SOLID BODY
17.1 Calculation of dynamic parameters
17.1.1 Generalities
17.1.2 The case of the translation movement
17.1.3 The case of rotational motion around a fixed point
17.1.4 The case of rotational motion around a fixed axis
17.1.5 The case of the plane-parallel movement
17.2 General theorems in the Dynamics of rigid solid body
17.3 General theorems in the relative movement of the rigid solid body towards
its
center of mass
17.4 Discussion on the general theorems
18. DINAMICS OF THE PARTICULAR MOVEMENTS OF THE RIGID
SOLID BODY
18.1 Translation movement
18.2 Rotational movement towards a fixed axis
18.2.1 System of equation
18.2.2 Equilibrating of the rotors
18.2.3 Physical pendulum
18.3 Rotational movement relative to a fixed point
18.3.1 System of equations
18.3.2 The gyroscope
18.3.3 Gyroscopic effect
18.4 Plan-parallel movement
19. DYNAMICS OF BODIES SYSTEMS
19.1 Generalities
19.2 The impulse method
19.3 The energy method
20. COLLISIONS AND PERCUSSIONS
20.1 Generalities
20.2 General theorems in the study of collisions
20.3 The centric collision of two spheres
20.4 Oblique collision of two spheres
20.5 Collision of a sphere with a fixed surface
20.6 Collision of a sphere with a rotating body
Part IV ANALYTICAL MECHANICS
21. PRINCIPLE OF D'ALEMBERT
21.1 The force of inertia
21.2 Torsor of inertia to rigid solid body
21.3. D'Alembert's principle of rigid solid body
21.4 The kinetostatic method in body systems
21.5 The kinetostatic method to the plane mechanisms
22. PRINCIPLE OF VIRTUAL MECHANICAL WORK
22.1 Links and displacements in Analytical Mechanics
22.2 Virtual mechanical work
22.3 Principle of virtual mechanical work in case of equilibrium
22.4 Principle of virtual mechanical work in the case of movement
23. LAGRANGE'S ECUATIONS
23.1 Abstractions in Analytical Mechanics
23.2 Equilibrium of systems with multiple degrees of freedom
23.3 Deduction of Lagrange's equations
23.4 Force function and dissipative function for usual cases
23.5 Applications of Lagrange's equations
23.5.1 Systems with a single degree of freedom
23.5.2 Systems with more degrees of freedom
24. DINAMICS OF OSCILLATING SYSTEMS
24.1 Generalities
24.2 The linear oscillator
24.3 Systems with a single degree of freedom
24.4 Systems with more degree of freedom
