The gyroscope is quoted as a mathematical gyroscope, that is, the intersecting lines of the equator and one meridian. The permissible movements of our mathematical gyroscope are the proper rotations of the equator and meridian circles and the rotation of the entire structure around the axis passing through the intersection points of the two circles. Since the proper rotations of the circles are specified by the group of diagonal matrices with complex units, and the rotation of the entire structure is specified by the group of special orthogonal matrices, it is expected that the group of motions of the mathematical gyroscope generated by these groups is equal to the unitary group U(2).
It is clear that this construction has a generalization in the form of a mathematical gyroscope of the n-dimensional sphere, which generates the group U(n). Does this construction find application in phenomenological theories of gauge symmetries?
gyro or rotation and central mass? Yes its how crystals form etcetera in mass phenomena...
It has many applications in Golf, Radar, and in particular tracking, e.g., via modern drone technology.
This construction can be applied to the question of the geometric origin of the internal symmetries of the Standard Model.
Indeed, it is easy to show that the symmetries of the motions of a mathematical gyroscope along the Hopf bundle, that is, along the bundle of the three-dimensional sphere, which is locally the product of a classical sphere and a circle, are described by the group SU(3)×SU(2)×U(1).
- Badges
- Science topic
- Similar topics
- Mathematics