Frame of reference, also called reference object,physicsA noun refers to a reference object or a system of objects that do not move relative to each other when studying the movement of objects.according toNewton's law of mechanicsWhether this is true in the reference system can be divided intoInertial frameandNon inertial frameTwo types.
The whole extended space connected with the reference body.The reference body is another object selected as the standard to determine the position of the object and describe its mechanical movement.In order to numerically express the position of an object, you can set a coordinate system on the reference body, which is called the reference coordinate system.Both the reference system and the reference coordinate system can be selected arbitrarily, but the expression of the same motion in different reference systems is different.The appropriate reference body is usually selected according to the actual situation of the problem.For example, when the rocket takes off from the earth's surface, the earth should be used as the reference body;When the spacecraft becomes an artificial planet moving around the sun, the sun should be used as the reference body.Thus, all mechanical phenomena can only be observed, described and studied relative to the selected reference system.There can be different reference coordinate systems on the same reference system. Although their values for the position coordinates of the same object are different, they are linked by certain geometric relations.In order to quantitatively describe the movement of objects, reference coordinate systems are often used directly.
Selection principle
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The choice of reference system is arbitrary, but it should be based on the principle of convenient observation and making the description of motion as simple as possible. The ground is often chosen as the reference system for studying the motion of objects on the ground.
If the general title is not specified, the reference system is the ground.
Selection of Reference System
1. Assume that the reference system does not move in advance.
2. Select different reference systems, and the results will be different.
3. The selection of reference system can be arbitrary.
4. Be in the same reference system.
Four properties
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Standardization: objects used as reference systems areAssume immobilityWhether the object under study is moving or stationaryRelative to Reference SystemFor.
Arbitrariness: The selection of reference system is arbitrary, but it should be based on the principle of convenient observation and simple description of motion.
Unity: When comparing different movements, you should chooseSame Reference System。
Difference: select different reference systems for the same movement, and observe the resultsGenerally different。For example, a passenger sitting in a moving car takes the ground as the reference system, and the passenger is moving, but if the car is taken as the reference system, the passenger is stationary.
importance
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If the position of the object relative to the reference system is changing, it indicates that the object is moving relative to the reference system;If the position of the object relative to the reference system is unchanged, it indicates that the object is stationary relative to the reference system.The same object is relative to different reference systems,motion state It can be different.staykinematicsThe selection of reference system can be arbitrary.The research and description of object motion can only be carried out after the reference system is selected.How to select the reference system must be considered from the specific situation.For example, when an interstellar rocket is launched, it mainly studies its movement relative to the ground, so the Earth is selected asobject of reference。However, when the rocket enters the orbit around the sun, the sun is selected as the reference system for the convenience of research.In order to study the movement of objects on the ground, it is most convenient to choose the earth as the reference system;If the ground is taken as the reference frame, the passengers are moving.Therefore, the choice of reference system is one of the keys to the research.
Research
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From the point of view of kinematics, the reference system can be arbitrarily selected.For a specific kinematics problem, we usually select a reference system from the convenience to simplify the research of object motion.In ancient times, when studying the movement of celestial bodies, it was natural to take the Earth as a reference system.Ptolemaic“Geocentric theory”Explain the motion of the planet with this wheel and even wheel.Copernicus“Heliocentric theory”When explaining the motion of the planet, the current wheel and the average wheel should also be used.From a kinematic point of view“Geocentric theory”And“Heliocentric theory”Can describe the motion of planets equally well.But from the perspective of studying the dynamic causes of planetary motion“Heliocentric theory”Opened the road to truth.Kepler“Geocentric theory”On the basis ofCircular motionKepler also established three laws of planetary motion on the basis of observation and made important contributions.Newton further revealed thatKepler's three lawsThe mystery ofLaw of universal gravitation, summarize“Universal gravitation”Concept.We should note that all reference systems are equal in terms of kinematics, and only consider whether it is easy to analyze and solve problems when selecting reference systems.From the perspective of dynamics, the reference system is divided intoinertiaReference system and non inertial reference system, Newton's law, etcDynamic lawIt is only valid for inertial reference systems, and it should be applied to different non inertial reference systemsNewton's lawThe corresponding inertial force correction shall be introduced.
particleThe mechanical motion of the particle is shown as the position of the particle changes with time.The position of the particle is relative to a certain reference system, which refers to a three-dimensional, non deformable object selected as the basis for studying object motion（rigid body）Or a group of objects as the reference body, select three non coplanar lines on the reference bodyIntersecting lineAsStandard frame, plus the clock fixed to the reference body.That is, the reference system includes the reference bodyStandard frameAnd clock, we are used to referring to the reference body as the reference system.In order to quantitatively describe the motion of objects, we also need to establishCoordinate system，Cartesian coordinatesandpolar coordinatesThey are the two most commonly used coordinate forms.
Newton called the reference system moving in a uniform straight lineinertiaReference system.In 1905, Einstein proposed in his paper that all inertiaReference systemAll are equivalent, that is to say, all physical laws are equally applicable and have the same form in the inertial reference system.Einstein's view is correct, because people cannot use any physical laws to find the difference between an inertial reference system and a stationary reference system in any inertial reference system (that is, without reference to objects outside the reference system).It was on this basis that Einstein establishedSpecial relativity。
So, if we are in a noninertiaWhat about in the reference system?The motion of non inertial reference frame has certain acceleration, but this acceleration can be regarded as a kind of gravity (also calledUniversal gravitation)。For example, when we are in an elevator, when the elevator accelerates to go down or decelerates to go up, we will feel a little light, and the weight seems to be reduced.We don't look outside in the elevatorobject of referenceI don't know whether the elevator is accelerating or decelerating, but I feel the gravity is changing.
In Newton's view, absolute motion is relative to an absolute stationary reference system.That is to say, there is an absolutely static space in nature, that is, absolute space.According to modern views, absolute space has no objective significance.In order to explain the contradiction between J.C. Maxwell's electromagnetic theory and the relativity principle in Newtonian mechanics, physicists in the 19th century assumed that space was filled with a massless and non flowing elastic medium "ether", and electromagnetic waves were regarded as the vibration of "ether".The reference system that is static relative to the "ether" represents the reference system that is absolutely static.The electromagnetic phenomena in this reference frame have special properties, which leads to the argument that the inertial coordinate system is unequal for describing electromagnetic phenomena.The famous experimental results published by A.A. Michelson and E.W. Morey in 1887 showed that the "ether" effect could not be detected.Later, other experiments also showed that the static reference system could not be found.Therefore,A. Einstein pointed out that there is no absolute stillness.
Einstein put forward two basic assumptions of special relativity, namely the principle of relativity and the invariance of the speed of light, in his famous paper "On the Electrodynamics of Moving Bodies" published in 1905.These two assumptions are the basis of special relativity. Many phenomena that cannot be explained by Newtonian mechanics can be accurately described by special relativity.Einstein's principle of relativity pointed out that the laws of physics, including mechanics, electrodynamics and optics, are the same in all inertial reference frames.That is, the inertial coordinate system is equal to the description of physical phenomena, and there is no special absolute static reference system, and the absolute space is meaningless.
Inertial reference frame
The reference system for the establishment of the inertial law is called inertial system for short.The relativity principle of classical mechanics points out that all mechanical laws are the same in a reference system that moves at a uniform speed without rotation.An observer in a sealed cabin moving at a uniform speed in a straight line cannot judge whether the cabin is stationary or moving at a uniform speed with respect to the star through internal mechanical experiments. He can only know if he looks out of the window, but still cannot determine whether the cabin or the star is moving.On the other hand, the mechanical equivalence of the reference system is not valid for any reference system in motion.In a bumpy train and a train in uniform motion, mechanical motion does not obey the same law.When accurately writing the equation of motion relative to the earth, the rotation of the earth must be considered.A reference system is called inertial reference system or Galileo reference system if a free particle moves in non accelerated motion. All reference systems that move in non accelerated motion without rotation are inertial reference systems.
Judging whether a specific reference system is an inertial system depends on how accurate the small acceleration effect of the reference system can be measured.In general engineering dynamics on the ground, due to the small rotation speed of the earth and the small centripetal acceleration of a point on the ground, the coordinate system fixed to the earth can be taken as the inertial reference system.In some problems that must include the rotation of the earth, for example, when studying the drift of gyro meters, the earth center coordinate system can be used as an approximate inertial reference system, with the origin coincident with the earth center and the axis pointing to the identified star.In astronomy, the ecliptic or galactic coordinate system is used as the inertial reference system.The centripetal acceleration of a point on the equator of the earth's surface is 3.4 cm/s2, the centripetal acceleration of the earth's revolution around the sun is 0.6 cm/s2, and the centripetal acceleration of the sun's rotation around the center of the Milky Way Galaxy is about 3 × 10-8 cm/s2.From the above data, we can see the approximation of the selected inertial reference system.
Non inertial test systems
The reference system that accelerates or rotates the inertial reference system is called non inertial reference system for short.
The non inertial system that is moving with constant acceleration α to the inertial system is called the accelerated motion reference system.In this reference system, the object at rest must be strongly acted by F=m α.In the gravitational field, objects are subject to gravity, so objects in the gravitational field whose inertial frame is stationary are also subject to gravity.If there is another non inertial system, its acceleration to the inertial system is the same as that generated by the gravity, then the observer in this non inertial system does not feel that there is a gravitational field, nor does he know that he has accelerated motion. This is Einstein's "elevator", which shows that the gravitational field and the non inertial system are equivalent.
The reference system that rotates to the inertial reference system is called the rotational reference system.Assuming that the inertial frame is stationary, the motion of the rigid body fixed to the rotating reference frame is the motion of the rotating reference frame to the inertial frame.[1]
Reference system and equivalence principle
The equivalence of inertial mass and gravitational mass is generally called the equivalence principle.This principle leads to a conclusion: an inertial reference system with gravitational field is equivalent to another non inertial reference system with accelerated motion, that is, internal physical experiments cannot distinguish between the two reference systems, which is Einstein's equivalence principle.Take Einstein's "elevator" as an example[2]If the lift is stationary in a uniform gravitational field of 1g, and in addition, it makes a uniform acceleration movement upward in free space at an acceleration of 9.81 m/s2, because the inertia mass and gravitational mass are equal, the same internal physical experiment results are made in the above two cases.The observer inside can think that the lift is stationary and there is a gravitational field in the car;It can also be considered that there is no gravitational field in the cabin, but the elevator is moving upward at an acceleration of 9.81 m/s2.
The equivalence of inertial mass and gravitational mass leads to another situation.If an object falls freely in a uniform gravitational field, the inertia force and gravity are in balance because the inertia mass and gravitational mass are equal.Therefore, the non rotating reference frame consolidated with the free falling object in the uniform gravitational field is equivalent to the inertial reference frame in free space.In spaceships flying around the earth, the phenomenon of "weightlessness" is caused by the balance of gravity and centrifugal inertial force.
The equivalence of inertial mass and gravitational mass is often called weak equivalence principle, while Einstein's equivalence principle is called strong equivalence principle.The principle of equivalence is the basis of general relativity.[3]
inertia
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From experience, we can always find such a reference system: its time passes evenly, and its space is uniform and isotropic;In such a frame of reference, the equation describing motion has the simplest form.Such a reference frame is an inertial frame.All inertial reference systems are equivalent.It is impossible to use mechanical experiments to determine whether the inertial reference frame in which it is located is moving in a uniform straight line.
Non inertial
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All reference systems that accelerate the inertial reference system are non inertial reference systems.
relative velocity
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The speed is different for different reference objects.The speed measured with the ground as the reference object is called absolute speed;The speed measured with a non ground reference system (such as air) is called relative speed.If trains A and B run in the same direction at the same speed, the speed of vehicle A relative to vehicle B and the speed of vehicle B relative to vehicle A are equal to zero;If driving in the opposite direction, the relative speed is equal to twice the speed.
In the same inertial reference system, suppose that one particle has a velocity of u1 and the other has a velocity of u2.Then the relative velocity is u2-u1.The relative velocity does not change with the selection of inertial reference system, that is, in Galileo transformation, the relative velocity is a constant vector, so the relative velocity also has a direction, which is the direction with large absolute value.
