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Gyroscope precession in special and general relativity from basic principles
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View: Figures


Image of Fig. 1.
Fig. 1.

A gyroscope transported around a circle. The vectors correspond to the central axis of the gyroscope at different times. The Newtonian version is on the left, the special relativistic version is on the right.

Image of Fig. 2.
Fig. 2.

A gyroscope transported along a circle at the photon radius of a static black hole. The gyroscope turns so that it always points along the direction of motion.

Image of Fig. 3.
Fig. 3.

A train at two consecutive times moving with velocity relative to a platform that accelerates upward. A gyroscope with a torque free suspension on the train will precess clockwise for .

Image of Fig. 4.
Fig. 4.

(a) The grid at rest with respect to . (b) The grid after a pure boost with velocity to the right, relative to . Note the length contraction. (c) The grid after a pure upward boost relative to a system that moves with velocity to the right. (d) The grid after a pure boost that stops the grid relative to .

Image of Fig. 5.
Fig. 5.

The stretch-induced tilt of the two points (the filled circles) due to the final stopping of the grid. The distance between the points prior to the stretching, as measured in the direction of motion, is denoted by .

Image of Fig. 6.
Fig. 6.

The real grid (black thin lines) and the corresponding imagined uncontracted grid (gray thick lines) before and after a large upward boost.

Image of Fig. 7.
Fig. 7.

A gyroscope grid at successive time steps. Both the grid and the gyroscope are depicted as they would be observed if they were uncontracted.

Image of Fig. 8.
Fig. 8.

Boost of the reference frame (of which the depicted thin grid is a small part) upward by a velocity . The velocity of the gyroscope grid is maintained.

Image of Fig. 9.
Fig. 9.

Relative to the gyroscope system, the reference frame (thin lines), of which we illustrate a certain part, rotates during the boost. The reference frame is depicted as it would appear if it was not length contracted relative to the gyroscope system.

Image of Fig. 10.
Fig. 10.

A train with a gyroscope moving relative to an accelerating platform observed at two successive times.

Image of Fig. 11.
Fig. 11.

A sketch of the rail and the train observed from an inertial system where the train is momentarily at rest.

Image of Fig. 12.
Fig. 12.

A free photon will in general follow a curved path relative to an accelerated reference frame. A gyroscope transported along such a path will keep pointing along the path if it did so initially.

Image of Fig. 13.
Fig. 13.

Sketch of the spatial geometry of a symmetry plane outside a black hole. The local static reference frame shown (the square grid) has a proper acceleration outward. For a sufficiently small such reference frame it works just like an accelerated reference frame in special relativity.

Image of Fig. 14.
Fig. 14.

Deviations from a straight line relative to a reference frame that accelerates in the direction. The plane shown is perpendicular to the momentary direction of motion (along the dashed line), and all the three vectors lie in this plane. The solid curving line is the particle trajectory. The thick line is the line that is fixed to the inertial system in question and is thus falling relative to the reference frame.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Gyroscope precession in special and general relativity from basic principles