Demonstration Aids for Euler's Rotation Theorem

Abstract

A demonstration teaching aid of Euler's rotation theorem belongs to the technical field of scientific education. The demonstration teaching aid of Euler's rotation theorem consists of a first device and a second device, wherein the first device is able to set a posture of a reference rigid body; after setting, a Euler axis position and a primary Euler rotation angle are obtained by measuring rotation angles of three rotations in the first device, and substituting the rotation angles into a direction cosine matrix for calculation; the second device is used for verifying the theorem; a corresponding position with respect to the angle obtained from the previous calculation is adjusted in the second device, so as to demonstrate the position of the Euler axis; the rigid body is returned to the initial posture by adjusting a spherical hinge; and then the rigid body in the initial posture is rotated around the Euler axis; if the rotation angle is the primary Euler rotation angle, the rigid body moves from the initial posture to the posture that is set in the first device, thereby the theorem is verified to be proved. The demonstration teaching aid of Euler's rotation theorem is more 'visual and intuitive' in demonstration effect; the determination way of the Euler axis does not affect the rotation among each portion of the devices; and the data can be read out at any time; the devices can be fixed after setting any position; the operation is simple; and the devices are portable.

Description

technical field [0001] The invention belongs to the technical field of science education, and in particular relates to a teaching aid for demonstrating Euler's rotation theorem. Background technique [0002] Euler's rotation theorem was formulated by the famous Swiss mathematician and physicist Leonhard Euler. Euler's rotation theorem is stated as follows: Any finite rotation of a rigid body around a fixed point can be realized by a rotation around a certain axis at that point. It can also be simply expressed as: the rotation of a rigid body from one posture to any posture can be realized by one rotation around a certain axis. The difficulties in understanding the theorem mainly lie in: first, how to find the axis of rotation, that is, the Euler axis; second, how to determine the rotation angle around the Euler axis, that is, the Euler primary rotation angle. [0003] At present, there are no teaching aids related to Euler's rotation theorem on the market. The explanation ...

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Problems solved by technology

[0003] At present, there are no teaching aids related to Euler's rotation theorem on the market. The explanation of Euler's rotation theorem in class is abstract and difficult to understand. The course progress is fast and the class content is monotonous. Students with pure theoretical knowledge are difficult to accept in a short time, and it takes a lot of time after class Self-taught understanding

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