The elements of mechanics

1 Phenomenic Reality and Models.- 2 Qualitative Aspects of the One-Dimensional Motion.- 3 Systems with Many Degrees of Freedom. Theory of the Constraints. Analytical Mechanics.- 4 Special Mechanical Systems.- 5 Stability Properties for Dissipative and Conservative Systems.- Appendices.- A. The Cauchy-Schwartz Inequality.- B. The Lagrange-Taylor Expansion.- D. Principle of the Vanishing Integrals.- E. Matrix Notations. Eigenvalues and Eigenvectors. A List of Some Basic Results in Algebra.- F. Positive-Definite Matrices. Eigenvalues and Eigenvectors. A List of the Basic Properties.- G. Implicit Function Theorems.- H. The Ascoli-Arzela Convergence Criterion.- L. Proof of Eq. (5.6.20).- M. Proof of Eq. (5.6.63).- N. The Analytic Implicit Function Theorem.- O. A Simple Algorithm for the Solutions of the Differential Equations. The Finite Difference Method.- P. Some Astronomical Data.- Definition and Symbols.- References.