The purpose of this work is to offer a clear physical explanation of the Coriolis force. Meterologists and oceanographers have invoked this somewhat mysterious force to explain the apparent equilibrium of a system of wind patterns or ocean currents in the presence of horizontal pressure gradients so that the velocity of fluid lies among isobars. The force is named for Gustave Gaspard Coriolis (1792-1843), a French mathematician who studied its effects. In order to make the mathematical concepts more tangible, the authors have prepared a series of computer exercises, written in BASIC for the IMB-AT with Enhanced Color Display, that can be copied piece by piece. For those who prefer not to make up their own copy of the program, there are instructions on how to order a pre-made copy in the Introduction of this book. These programs will provide an interactive tool for experimenting with a variety of problems involving the idea of Coriolis force. "An Introduction to the Coriolis Force" will be most useful for studying the hydrodynamics of the ocean and atmosphere. It also presents many aspects of classical mechanics/dynamics physics.
Its straightforward explanations and unique accessibility should help explain the complexities of this mysterious force, about which many scientists have had lingering uncertainties since it was first described in 1831.
AcknowledgementsIntroductionProlegomenonI. Real and apparent force1.1 Real force1.1 Apparent forceExercisesConventions about notationII. Velocity and acceleration in plane polar coordinates2.1 Transformation of coordinates2.2 Velocity and accelerationExercisesIII. Rotating coordinate frames3.1 Coriolis force3.2 Magnitude of the Coriolis force3.3 Centrifugal and Coriolis forces in rotating rectangular coordinates3.4 Experts, novices and Hooke springs3.5 Trajectories in the absolute inertial reference frame3.6 A linkage analogy3.7 Trajectory in rotating frame3.8 Another approach using complex notation3.9 The usage of the words "balance" and "equilibrium"ProblemsExercisesSome physical interpretation of what we have observed in exercise 3-1IV. The paraboloidal dish4.1 The paraboloid as a platform4.2 Small amplitude motions in the rotating frame4.3 First integralsProblemsExercisesV. Surfaces of revolution5.1 Hemispherical and paraboloidal dishes compared5.2 Comparison with the Hooke spring plane5.3 Results from first integrals5.4 The paraboloid5.5 The Hooke spring plane5.6 Spherical dish5.7 Rotation of the apsides5.8 Numerical solutionsProblemsExercisesVI. Velocity and acceleration in spherical coordinates6.1 Tranformation from cylindrical polar coordinates to spherical coordinates6.2 Alternative forms in inertial space6.3 Acceleration and Coriolis forces in rotating spherical coordinates6.4 Trajectories on the surface of a gravitating sphere6.5 Planer motion in spherical coordinatesProblemsExercisesVII. Huygen's rotating oblate earth7.1 Approximate figure of the earth7.2 Forces on a plumb bob7.3 Computing the bulge7.4 Novice particles on Huygen's spheroid7.5 Free fall from a short tower7.6 Calculation of the deflection of a falling particle in a rotating coordinate frame7.7 Fall from a tower calculated in inertial space7.7a Preliminary results regarding ellipses7.7b Freely falling particleProblemsExercisesSome further thought about the exercises of chapter 7VIII. Forced motion8.1 Real forces relative to the rotating system8.2 Balances among terms8.3 Response of a particle to a force of the first typeExercisesIX Refining the earth's platform9.1 Deficiencies of the Huygen's spheroid9.2 Combined centrifugal and gravitational potentials9.3 The concept of a platform as an equipotential surface9.4 Maclaurin's ellipsoid9.5 Particle motions on the Maclaurin ellipsoidProblemExercisesX. Concluding Materials10.1 General References--other places to look10.2 A vector derivation10.3 Size of accelerations and forces in terrestrial fluids10.4 Pressure gradiantsAppendix--The Compton generatorA.1 Historical backgroundA.2 Computation of flow in the Compton experiementA.3 Do it yourselfA.4 The Compton generatorA.5 Computation (1). Rotating reference frameA.6 Computation (2). As seen in intertial spaceA.7 Compton saves himselfExerciseEpilogue--Sample of the screen: Example 7-1Index
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