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CHAPTER V.
GENERAL EQUATIONS OF DYNAMICS.
| Article | Page | |
|---|---|---|
| 553. | Lagrange’s method Joseph-Louis Lagrange (1736–1813) developed a way to describe mechanical systems using generalized coordinates rather than simple physical positions. provides the necessary framework for studying advanced dynamical sciences | 184 |
| 554. | These mathematical concepts must be translated into the language of physical dynamics | 184 |
| 555. | Degrees of freedom The number of independent ways a system can move. of a connected system | 185 |
| 556. | Generalized meaning of velocity | 186 |
| 557. | Generalized meaning of force | 186 |
| 558. | Generalized meaning of momentum and impulse | 186 |
| 559. | Work performed by a small impulse | 187 |
| 560. | Kinetic energy expressed in terms of momenta (Tp) | 188 |
| 561. | Hamilton’s equations of motion A reformulation of classical mechanics developed by William Rowan Hamilton. | 189 |
| 562. | Kinetic energy expressed in terms of both velocities and momenta (Tp q̇) | 190 |
| 563. | Kinetic energy expressed in terms of velocities (Tq̇) | 191 |
| 564. | Relationships between Tp and Tq̇, and between momentum (p) and velocity (q̇) | 191 |
| 565. | Moments and products of inertia and mobility | 192 |
| 566. | Necessary conditions that these coefficients must satisfy | 193 |
| 567. | The relationship between mathematical, dynamical, and electrical concepts | 193 |
CHAPTER VI.
APPLICATION OF DYNAMICS TO ELECTROMAGNETISM.
| 568. | The electric current possesses energy | 195 |
| 569. | The current is a kinetic phenomenon Meaning it involves the motion of matter or a medium. | 195 |
| 570. | Work performed by electromotive force | 196 |
| 571. | The most general expression for the kinetic energy of a system that includes electric currents | 197 |
| 572. | Electrical position variables do not appear in this expression | 198 |
| 573. | Mechanical force acting on a conductor | 198 |
| 574. | Evidence that terms involving the product of ordinary velocities and current strengths do not exist | 200 |
| 575. | Another experimental test | 202 |
| 576. | Discussion regarding electromotive force | 204 |
| 577. | If terms involving products of velocities and currents existed, they would create electromotive forces that are not actually observed | 204 |
CHAPTER VII.
ELECTROKINETICS.
| 578. | The electrokinetic energy of a system of linear circuits | 206 |
| 579. | Electromotive force in each individual circuit | 207 |
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