The following examples, amongst others, to be taken as applications or subjects of exercises relative to the general principles which precede.
Walking. Recoil of guns. Eolypile. Flight of rockets.
Pressure of fluid veins, resistance of mediums, &c. Direct collision of bodies more or less hard, elastic, or penetrable. Exchange of quantities of motion. Loss of vis viva under different hypotheses. Influence of vibrations and permanent molecular displacements.
Pile driving; advantage of large rammers. Comparison of effects of the shocks and of simple pressures due to the weight of the construction. Oblique collision, and ricochet. Data furnished by experiment.
Oscillations of a vertical elastic prism suspended to a fixed point, and loaded with a weight, neglecting the inertia, and the weight of the material parts of this prism. Case of a sudden blow. What is meant by the “resistance vive” of a prism to rupture? Results of experiments.
Work developed by powder upon projectiles, estimated according to the vis viva which it impresses on them, as well as upon the gun and the gases upon hypothesis of a mean velocity.
SPECIAL DYNAMICS OF SOLID BODIES.
Lessons 9–12. Simple Rotation of an invariable Solid about its Axis.
In applying to this case the first general rule of dynamics, the theorem of the moments of the quantities of motion, and the theorem of work, we are led to the notion of the moment of inertia; explanation of the origin of this name. The angular acceleration is equal to the sum of the moments of the exterior forces divided by the moment of inertia about the axis of rotation. Sum of the moments of the quantities of motion relative to this axis. Vis viva of a solid simply turning about an axis. What is meant by radius of gyration?
Remind of the geometrical properties of moments of inertia, of the ellipsoid which represents them, of the principal axes at any point, of those which are referred to the center of gravity.