Caius Iacob: Applied mathematics and mechanics

Section 1. Forces and their vector representation.
Section 2. Elements of vector algebra.
Section 3. Applications.
Section 4. Reduction of systems of forces applied to a rigid body.
Section 5. Parallel forces.
Section 6. Equilibrium conditions for a rigid body. The beam subject to continuous loads and concentrated loads.
Section 7. Appendix. Primitives and the NewtonLeibniz formula.
Chapter II. Elements of the geometry of masses.
Section 1. Addition of parallel gravity forces.
Section 2. Applications to triangle geometry.
Section 3. Some properties of the tetrahedron.
Section 4. Other geometrical applications.
Section 5. Some inadequate definitions in geometry.
Chapter III. Moments of inertia.
Section 1. Moments of inertia with respect to a point.
Section 2. Geometrical applications.
Section 3. Euler's theorem for quadrangles and extensions.
Section 4. Moments of inertia with respect to an axis.
Section 5. Moments of inertia with respect to a plane.
Section 6. Generalizations concerning the tensor of inertia of a system of mass points.
Section 7. A generalization of the theory of moments of inertia.
Section 8. Geometrical applications.
Section 9. On some geometrical locus problems.
Section 10. A new extension of theorems of Lagrange and Leibniz. Geometrical applications.
Chapter IV. Some consequences of the theory of reduction of forces applied to a rigid body.
Section 1. Applications of Varignon's theorem.
Section 2. Geometric properties with mechanical significance.
Section 3. Other geometrical applications.
Section 4. The theorem of Lazare Carnot and some of its corollaries.
Chapter V. Applications of integral calculus to the determination of the centres of gravity and moments of inertia of some geometric bodies.
Section 1. Determination of the centres of gravity.
Section 2. Calculation of the moments of inertia of some bodies with respect to an axis.
JOC/EFR April 2007
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