Gravity train

Abstract: A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can attain speeds arbitrarily close to the speed of light; generalizing the electrostatic and gravitational cases requires special and general relativity, respectively. We find exact closed-form relations between the position, proper time, and coordinate time in both cases, and find that they are no longer harmonic, with oscillation periods that depend on the amplitude. In the highly relativistic limit of both cases, the particle spends almost all of its proper time near the turning points, but almost all of the coordinate time moving through the bulk of the ball. Buchdahl's theorem imposes nontrivial constraints on the general-relativistic case, as a ball of given density can only attain a finite maximum radius before collapsing into a black hole. This article is intended to be pedagogical, and should be accessible to those who have taken an undergraduate course in general relativity.

Abstract: The invention discloses a gravity train system, and in particular relates to a train system taking gravity as main force application source for accelerating and braking as well as a running method of the system. The gravity train system comprises a gravity train and a gravity train track, wherein the gravity train comprises a gravity train carriage which can run on a line with a high gradient and a long ramp, and a running resistance balancing engine with low power; the gravity train track comprises a steep long downhill gradient, a steep long uphill gradient, a middle transitional channel, a station track and a gravity starting track; a horizontal plane passing through the lowest point of the middle transitional channel is taken as a reference plane, so that the heights of the upper ends of the steep long downhill gradient and the steep long uphill gradient which are above the reference plane are the same. The acceleration thrust for gravity train running is mainly obtained by doing positive work on the basis of the gravity, namely converting the gravity potential energy into dynamic energy, and the deceleration braking of the gravity train is mainly realized by doing negative work on the basis of the gravity, namely converting the dynamic energy into the gravity potential energy, so that energy consumption can be greatly reduced.

Abstract: The utility model discloses a gravity train system, and in particular relates to a train system with the gravity as a main accelerating and braking force applying source The gravity train system comprises a gravity train and a gravity train track The gravity train comprises a gravity train carriage and a low-power balance running resistance engine, wherein the gravity train carriage runs on a route with a large slope and a long ramp; and the gravity train track comprises a long and steep down-ramp, a long and steep up-ramp, a middle transition channel, a platform track and a gravity starting track, wherein the horizontal plane passing through the lowest point of the middle transition channel is used as a reference surface, and the heights of the upper ends of the long and steep down-ramp and the long and steep up-ramp, which are located above the reference surface, are same The acceleration thrust for promoting the gravity train to run is mainly obtained through positive power acted by the gravity, ie, kinetic energy converted from gravitational potential energy, the reduction braking of the gravity train is mainly realized by means of the negative power acted by the gravity, ie, the gravitational potential energy converted from the kinetic energy, and thus, a great deal of energy consumption can be reduced