CN115691277A - Teaching tool for Lagrange point concept - Google Patents

Abstract

The invention discloses a teaching tool for Lagrange point concepts, and relates to the technical field of physics and astronomy teaching appliances. The invention relates to a teaching tool for Lagrange point concept, which has good teaching display effect.

Description

Teaching tool for Lagrange point concept

Technical Field

The invention relates to the technical field of physics and astronomy, in particular to a teaching tool aiming at Lagrangian point concepts.

Background

The Lagrange point is an astronomy and mechanics abstract concept, and is five special solutions of a restrictive three-body problem in astronomy. A small object is under the attractive force of two large objects at a point in space where it remains substantially stationary relative to the two large objects. The existence of these points was deduced by the Swiss mathematician Euler in 1767, and the French mathematician Lagrangian in 1772 deduced that there were two. Two of the 5 lagrangian points are stable (L4, L5), i.e., small objects tend to remain in place at this point even if disturbed by external gravitational forces. Each stable point and the point where the two large objects are located form an equilateral triangle.

When introducing special positions of some detectors to students and audiences, the special positions can be described by using inaccurate words such as 'space parking spaces'. In daily teaching and scientific popularization work, the Lagrange point is an abstract knowledge point and is also a difficult point.

The patent aims to solve the problem that a model for visual display is lacked in teaching, provides a teaching tool for the Lagrangian point concept, is also suitable for astronomy and mechanics teaching activities serving vision disorder groups, and therefore provides the teaching tool for the Lagrangian point concept.

Disclosure of Invention

The invention mainly aims to provide a teaching tool for Lagrangian point concepts, which can effectively solve the problem that students are difficult to understand in the existing Lagrangian point teaching process in the background technology.

In order to achieve the purpose, the invention adopts the technical scheme that: a teaching tool for a Lagrange point concept comprises a Lagrange point model main body, wherein the Lagrange point model main body is of a hemispherical structure integrally, a first through hole and a second through hole are formed in the Lagrange point model main body, the central axis of the first through hole is aligned to the central axis of the Lagrange point model main body, the second through hole is formed in one side of the first through hole, the diameter of the first through hole is larger than that of the second through hole, the corner at the upper end of the first through hole is subjected to circular arc processing, the corner at the upper end of the second through hole is subjected to circular arc processing, and different colors are printed on different stars on the Lagrange point model main body.

Preferably, the outer wall of the lagrangian point model main body is provided with a plurality of grooves, the grooves are distributed in an equidistant array mode, all points are equal in height, the grooves are used as equipotential lines, the lagrangian point model main body adopts a three-dimensional model mode to display a potential energy curved surface and a corresponding relation between a point (an extreme point) with a potential energy derivative being zero and the lagrangian point, the equal-height grooves are used as equipotential surfaces for teaching, and an equipotential surface diagram shown in fig. 3 is printed to display the height of the gravitational potential energy.

Preferably, a first point, a second point, a third point, a fourth point and a fifth point are marked on the lagrangian model main body, the first point, the second point and the third point are located on the same straight line L, and the fourth point and the fifth point are respectively located on two sides of the straight line L and are symmetrically distributed about the straight line L.

Preferably, a ball is placed at the first point, the second point, the third point, the fourth point and the fifth point.

Preferably, the small balls are made of iron, the small ball simulation spacecraft model is more convenient to teach by arranging the small ball simulation spacecraft model, students can visually know the positions and the functions of the five Lagrangian points, and the teaching effect is improved.

Preferably, magnets are respectively embedded under the first point, the second point, the third point, the fourth point and the fifth point, and the magnets and the small balls generate magnetic attraction force to place the small balls representing the planet balls and show the stability of the spacecraft in parking near the lagrangian point. The teaching aid is manufactured into a large sculpture, and allows audiences to climb and stand and feel the gradient and the stability of different positions. The teaching aid of this patent also can supply the student to touch, feels the stability of berthing the position behind the perturbation.

Preferably, the Lagrange model main body is integrally printed by a 3D printer, the method and the device can not only print a miniature model through the 3D printer to provide students with visit, but also manufacture a large-scale wood sculpture to allow the students to climb and stand and feel the gradient and the stability of different positions. The teaching aid of this patent also can supply the student to touch, feels the stability of berthing the position behind the perturbation.

Preferably, the coordinates of the first point are:

the coordinates of the second point are:

the coordinates of the third point are:

the coordinates of the fourth point are:

the coordinates of the fifth point are:

wherein M and M2 are the mass of the celestial body, R is the orbit radius of the rotation of M2 around M, and a is M2/(M + M2).

Compared with the prior art, the invention has the following beneficial effects:

according to the method, a Lagrange point model main body is arranged, a plurality of grooves are formed in the outer wall of the Lagrange point model main body and distributed in an equidistant array mode, all points are equal in height through the grooves, the groove lines serve as equipotential lines, the Lagrange point model main body adopts a three-dimensional model to display a potential energy curved surface and the corresponding relation between points (extreme points) with potential energy derivatives being zero and Lagrange points, the equal-height grooves serve as equipotential surfaces for teaching, an equipotential surface graph shown in a figure 3 is printed, and the height of gravitational potential energy is displayed.

In the present invention, by in five la lambertian points: the magnets are embedded below the first point, the second point, the third point, the fourth point and the fifth point, so that the aerospace model is more convenient to teach when an iron small ball is used, students can visually know the positions and the functions of the five Lagrange points, and the teaching effect is improved.

Drawings

FIG. 1 is a schematic diagram of the overall structure of a teaching tool for Lagrangian point concept of the present invention;

FIG. 2 is a schematic diagram showing the positional relationship between two lagrangian points, M1, M2 and 5, in a teaching tool for the Lagrangian point concept of the present invention;

FIG. 3 is a schematic diagram of equipotential surfaces in a teaching tool for the Lagrangian point concept of the present invention;

FIG. 4 is a cross-sectional view of a first point in the teaching tool for the Lagrangian point concept of the present invention;

FIG. 5 is a cross-sectional view of a second point in the teaching tool for the Lagrangian point concept of the present invention;

FIG. 6 is a cross-sectional view of a third point in the teaching tool for the Lagrangian point concept of the present invention;

fig. 7 is a cross-sectional view of a fourth point and a fifth point of the teaching tool for the lagrangian point concept of the present invention.

In the figure: 1. a lagrange point model body.

Detailed Description

In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further explained by combining the specific embodiments.

In the description of the present invention, it should be noted that the terms "upper", "lower", "inner", "outer", "front", "rear", "both ends", "one end", "the other end", and the like indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.

In the description of the present invention, it should be noted that, unless explicitly stated or limited otherwise, the terms "mounted," "disposed," "connected," and the like are to be construed broadly, such as "connected," which may be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.

Referring to fig. 1-7, the invention relates to a teaching tool for lagrangian point concepts, which comprises a lagrangian point model main body 1, wherein the lagrangian point model main body 1 is of a hemispherical structure as a whole, a first through hole and a second through hole are formed in the lagrangian point model main body 1, the central axis of the first through hole is aligned with the central axis of the lagrangian point model main body 1, the second through hole is positioned on one side of the first through hole, the diameter of the first through hole is larger than that of the second through hole, the corner at the upper end part of the first through hole is subjected to arc treatment, and the corner at the upper end part of the second through hole is subjected to arc treatment, and different colors are printed on different stars on the lagrangian point model main body 1.

The outer wall of the Lagrange point model main body 1 is provided with a plurality of grooves, the grooves are distributed in an equidistant array mode, all points are equal in height through the grooves, the grooves are used as equipotential lines, the Lagrange point model main body 1 adopts a three-dimensional model mode to display a potential energy curved surface and a corresponding relation between a point (an extreme point) with a potential energy derivative being zero and a Lagrange point, the equal-height grooves are used as equipotential surfaces for teaching, and the equipotential surface diagram shown in figure 3 is printed to display the strength potential energy.

The lagrangian model main body 1 is marked with a first point, a second point, a third point, a fourth point and a fifth point, the first point, the second point and the third point are located on the same straight line L, and the fourth point and the fifth point are respectively located on two sides of the straight line L and are symmetrically distributed about the straight line L.

Wherein, the first point, the second point, the third point, the fourth point and the fifth point are provided with small balls.

The material of bobble is iron, and bobble simulation spacecraft model is through setting up the more convenient teaching of bobble simulation spacecraft model ware, can make the audio-visual position and the effect of knowing five lagrangian points of student, improves the teaching effect.

Magnets are embedded under the first point, the second point, the third point, the fourth point and the fifth point respectively, and the magnets and the small balls generate magnetic attraction force to place the small balls representing the planet balls and show the stability of the spacecraft in parking near the Lagrange point. The teaching aid is manufactured into a large sculpture, allows audiences to climb and stand, and feels the gradient and the stability of different positions. The teaching aid of this patent also can supply the student to touch, feels the stability of berthing the position behind the perturbation.

The Lagrange model main body 1 is integrally printed by the 3D printer, and the three-dimensional model can be printed by the 3D printer to provide students with visions, can also be used for manufacturing large-scale wooden sculptures, allows the students to climb and stand, and feels the gradient and the stability of different positions. The teaching aid of this patent also can supply the student to touch, feels the stability of berthing the position behind the perturbation.

Wherein the coordinates of the first point are:

the coordinates of the second point are:

the coordinates of the third point are:

the coordinates of the fourth point are:

the coordinates of the fifth point are:

wherein M1 and M2 are the mass of the celestial body, R is the orbit radius of the rotation of M2 around M1, and a is M2/(M1 + M2).

The working principle of the invention is as follows: referring to fig. 1 to 7, in the teaching tool for the lagrangian point concept, in the using process, the equipotential surfaces and the equipotential lines are displayed through the grooves serving as the equipotential lines, so that students can conveniently view the potential energy of the lagrangian points, and the potential energy of the lagrangian points is obtained through the following steps: the magnets are embedded below the first point, the second point, the third point, the fourth point and the fifth point, so that the aerospace model is more convenient to teach when an iron small ball is used, students can visually know the positions and the functions of the five Lagrange points, and the teaching effect is improved.

The foregoing shows and describes the general principles and broad features of the present invention and advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (8)

1. A teaching tool for lagrangian point concepts, characterized by: the lagrangian point model comprises a lagrangian point model main body (1), wherein the lagrangian point model main body (1) is of a hemispherical structure as a whole, a first through hole and a second through hole are formed in the lagrangian point model main body (1), the central axis of the first through hole is aligned with the central axis of the lagrangian point model main body (1), the second through hole is located on one side of the first through hole, the diameter of the first through hole is larger than that of the second through hole, the corner of the upper end part of the first through hole is subjected to circular arc treatment, and the corner of the upper end part of the second through hole is subjected to circular arc treatment.

2. The teaching tool for lagrangian point concepts according to claim 1, wherein: the outer wall of the Lagrange point model main body (1) is provided with a plurality of grooves, the grooves are distributed in an equidistant array mode, and all points are equal in height through the grooves.

3. A teaching tool for lagrangian point concepts according to claim 2, characterized in that: the Lagrange point model main body (1) is marked with a first point, a second point, a third point, a fourth point and a fifth point, wherein the first point, the second point and the third point are positioned on the same straight line L, and the fourth point and the fifth point are respectively positioned on two sides of the straight line L and are symmetrically distributed about the straight line L.

4. The teaching tool for lagrangian point concepts of claim 3, wherein: and small balls are placed at the first point, the second point, the third point, the fourth point and the fifth point.

5. The teaching tool for lagrangian point concepts of claim 4, wherein: the material of pellet is iron, pellet simulation spacecraft model.

6. The teaching tool for lagrangian point concepts of claim 5, wherein: magnets are embedded under the first point, the second point, the third point, the fourth point and the fifth point respectively, and the magnets and the small balls generate magnetic attraction.

7. The teaching tool for lagrangian point concepts of claim 6, wherein: the Lagrange point model main body (1) is integrally printed by a 3D printer.

8. The teaching tool for lagrangian point concepts of claim 7, wherein: the coordinates of the first point are:

the coordinates of the second point are:

the coordinates of the third point are:

the coordinates of the fourth point are:

the coordinates of the fifth point are:

wherein M1 and M2 are the mass of the celestial body, R is the orbit radius of the rotation of M2 around M1, and a is M2/(M1 + M2).

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