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Biblioteka Wirtualna Matematyki
Monografie Matematyczne
Tom 24
Mechanics
Stefan Banach
Warszawa-Wrocław 1951
I. Operations on vectors§ 1. Preliminary definitions§ 2. Components of a vector§ 3. Sum and difference of vectors§ 4. Product of a vector by a number§ 5. Components of asum and product
§ 6. Resolution of a vector§ 7. Scalar product
§ 8 Vector product
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CHAPTER III
DYNAMICS OF A MATERIAL POINT
I. Dynamics of an unconstrained point§ 1. Basic concepts of dynamics§ 2. Newton's laws of dynamics
§ 3. Systems of dynamical units§ 4. Equations of motion§ 5. Motion under the influence of the force of gravity§ 6. Motion in a resisting medium§ 7. Moment of momentum§ 8. Central motion
§ 9. Planetary motions§ 10.Work§ 11. Potential force field§ 12. Examples of potential fields§ 13. Kinetic and potential energy§ 14. Motion of a point attracted by af ixed mass
§ 15. Harmonic motion§ 16. Conditions for equilibrium in aforcefield
II. Dynamics of a constrained point§ 17. Equations of motions§ 18. Motion of a constrained point along a curvece§ 19. Motion of a constrained point along a surface
§ 20. Mathematical pendulum
§ 21. Equilibrium of a constrained pointIII. Dynamics of relative motion§ 22. Laws of motion§ 23. Examples of motion§ 24. Relative equilibrium
§ 25. Motion relative to the earth
I. Systems of points§ 1.Statical moments
§ 2. Centre of mass
§ 3 Moments of the second order
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§ 14. Conditions of equilibrium§ 15. Systems of bars§ 16. Frames
§ 17. Equilibrium of heavy cables
CHAPTER VII
KINEMATICS OF A RIGID BODY
§ 1. Displacement and rotation of a body about an axis
§ 2. Displacements of points of a body in plane motion§ 3. Displacements of the points of a body§ 4. Advancing motion and rotation about an axis§ 5. Distribution of velocities in a rigid body§ 6. Instantaneous plane motion§ 7.Instantaneous space motion
§ 8. Rolling and sliding§ 9. Composition of motions of a body§ 10. Analytic representation of the motion of a rigid body§ 11. Resolution of accelerations
CHAPTER VIII
DYNAMICS OF A RIGID BODY
§ 1. Work and kinetic energy§ 2. Equations of motion§ 3. Rotation about a fixed axis§ 4. Plane motion§ 5.Angular momentum
§ 6. Euler's equations§ 7. Rotation of a body about a point under the action of no forces§ 8. Rotation of a heavy body about a point§ 9. Motion of a sphere on a plane§ 10. Foucault's. gyroscope
CHAPTER IX
PRINCIPLE OF VIRTUAL WORK
§ 1. Holonomo-scleronomic systems§ 2.Virtual displacements§ 3. Principle of virtual work
§ 4. Determination of the position of equilibrium in a force field§ 5. Lagrange's generalized coordinates
§ 1. Holonomic systems§ 2 N h l i t
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