Примеры использования Proper acceleration на Английском языке и их переводы на Русский язык
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The shape of the invariant hyperbola corresponds to a path of constant proper acceleration.
Gravitation therefore doesnot cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from.
A corollary is that all inertial observers always have a proper acceleration of zero.
In relativity theory, proper acceleration is the physical acceleration(i.e., measurable acceleration as by an accelerometer) experienced by an object.
Hence the change in proper-velocity w=dx/dτ is the integral of proper acceleration over map-time t i.e. Δw=αΔt for constant α.
Thus the distinction between proper-acceleration and coordinate acceleration allows one to track the experience of accelerated travelers from various non-Newtonian perspectives.
At low speeds in the inertial coordinate systems of Newtonian physics, proper acceleration simply equals the coordinate acceleration a=d2x/dt2.
Proper acceleration contrasts with coordinate acceleration, which is dependent on choice of coordinate systems and thus upon choice of observers see three-acceleration in special relativity.
That downward acceleration becomes coordinate if we inadvertently step off a cliff into a zero proper-acceleration(geodesic or rain-frame) trajectory.
The value used is generally the local proper acceleration(which diverges at the event horizon) multiplied by the gravitational time dilation factor which goes to zero at the event horizon.
Only in such situations is coordinate acceleration entirely felt as a g-force i.e. a proper acceleration, also defined as one that produces measurable weight.
At a given instant in our frame,the observer frame, both spaceships accelerate in the same direction along the line between them with the same constant proper acceleration.
If one chooses to recognize that gravity is caused by the curvature of spacetime(see below), proper acceleration differs from coordinate acceleration in a gravitational field.
In each of these cases, physical or proper acceleration differs from coordinate acceleration because the latter can be affected by your choice of coordinate system as well as by physical forces acting on the object.
Therefore, the magnitude of the four-acceleration(which is an invariant scalar)is equal to the proper acceleration that a moving particle"feels" moving along a worldline.
Proper acceleration reduces to coordinate acceleration in an inertial coordinate system in flat spacetime(i.e. in the absence of gravity), provided the magnitude of the object's proper-velocity(momentum per unit mass) is much less than the speed of light c.
If the ground is removed and the observer allowed to free-fall,the observer will experience coordinate acceleration, but no proper acceleration, and thus no g-force.
The total(mechanical) force that is calculated to induce the proper acceleration on a mass at rest in a coordinate system that has a proper acceleration, via Newton's law F m a, is called the proper force.
The proper distance to the horizon is finite, so the length of rope needed would be finite as well, but if the rope were lowered slowly(so thateach point on the rope was approximately at rest in Schwarzschild coordinates), the proper acceleration(G-force) experienced by points on the rope closer and closer to the horizon would approach infinity, so the rope would be torn apart.
In an inertial frame in which the object is momentarily at rest, the proper acceleration 3-vector, combined with a zero time-component, yields the object's four-acceleration, which makes proper-acceleration's magnitude Lorentz-invariant.
In situations in which gravitation is absent but the chosen coordinate system is not inertial, but is accelerated with the observer(such as the accelerated reference frame of an accelerating rocket, or a frame fixed upon objects in a centrifuge),then g-forces and corresponding proper accelerations felt by observers in these coordinate systems are caused by the mechanical forces which resist their weight in such systems.
The"acceleration of gravity"("force of gravity")never contributes to proper acceleration in any circumstances, and thus the proper acceleration felt by observers standing on the ground is due to the mechanical force from the ground, not due to the"force" or"acceleration" of gravity.
In the unidirectional case i.e. when the object's acceleration is parallel orantiparallel to its velocity in the spacetime slice of the observer, proper acceleration α and coordinate acceleration a are related through the Lorentz factor γ by α=γ3a.
For example, an object subjected to physical or proper acceleration ao will be seen by observers in a coordinate system undergoing constant acceleration aframe to have coordinate acceleration: a→ a c c a→ o- a→ f r a m e{\displaystyle{\vec{ a}}_{ acc}={\ vec{ a}}_{ o}-{\ vec{a}}_{frame.
Generally, objects in such a fall or generally any such ballistic path(also called inertial motion), including objects in orbit,experience no proper acceleration neglecting small tidal accelerations for inertial paths in gravitational fields.
In an accelerating rocket after launch, oreven in a rocket standing at the gantry, the proper acceleration is the acceleration felt by the occupants, and which is described as g-force(which is not a force but rather an acceleration; see that article for more discussion of proper acceleration) delivered by the vehicle only.
In the standard inertial coordinates of special relativity, for unidirectional motion, proper acceleration is the rate of change of proper velocity with respect to coordinate time.
This, along with diligent avoidance of unaccelerated frames,allows them to treat proper and coordinate acceleration as the same thing.
Two observers in Minkowski spacetime accelerate with constant magnitude k{\displaystyle k} acceleration for proper time σ{\displaystyle\sigma} acceleration and elapsed time measured by the observers themselves, not some inertial observer.
The acceleration of the body, after proper calibration, measured in units of acceleration of gravity g.