Newton's laws of motion and his universal law of gravitation described mathematically the motion of two bodies undergoing mutual gravitational attraction. However, it is impossible to solve analytically the equation of motion for three gravitationally interacting bodies. This book discusses some techniques used to obtain numerical solutions of the equations of motion for planets and satellites, which are of fundamental importance to solar-system dynamicists and to those involved in planning the orbits of artificial satellites. The first part introduces the classical two-body problem and solves it by rigorously developing the six integrals of the motion, starting from Newton's three laws of motion and his law of gravitation and then using vector algebra to develop the integrals. The various forms of the solution flow naturally from the integrals. In the second part, several modern perturbation techniques are developed and applied to cases of practical importance. For example, the perturbed two-body problem for an oblate planet or for a nonsymmetric rotating planet is considered, as is the effect of drag on a satellite. The two-body problem is regularized, and the nonlinear differential equation is thereby transformed to a linear one by further embedding several of the integrals. Finally, a brief sketch of numerical methods is given, as the perturbation equations must be solved by numerical rather than by analytical methods.
This pedagogically rich text has all the necessary features to ''hook'' introductory students and keep them interested and successful in preparatory chemistry. This book carefully guides beginning students through the fundamental principals and calculations required for their subsequent success in either the general chemistry course or the short organic and biochemistry course. Krimsley, while dedicated to conceptual understanding and skill building, presents a solid book that provides students with complete explanations on every point and helps them work through the material methodically, with many examples and hints. His approach is cohesive and coherent, always patient and interesting. Krimsley introduces all topics through an example students are already familiar with. He continually reminds them of objectives, and provides many opportunities to practice and then check their answers. The text begins with a study of atomic and molecular structure prior to treating the various categories of chemical reactions. The organization is designed to ''get students'' into chemistry quickly yet methodically. The classification of matter begins in Chapter 2, before the chapter on measurement, and the coverage of bonding appears in Chapter 8. The elementary concepts of chemistry are presented with an emphasis on mathematical calculations and problem-solving strategies.
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