A Newtonian system is a physical system that follows the laws of classical mechanics, as described by Sir Isaac Newton's laws of motion.
A trivial bundle is a mathematical concept that refers to a product space where each point in one space is paired with a unique point in another space. In other words, it is a set of points that can be described as a direct product of two spaces.
In the context of classical mechanics, a Newtonian system can be mathematically represented as a trivial bundle, with the base space being the configuration space and the fiber space being the velocity space.
This is because the mathematical description of classical mechanics, including Newton's laws of motion, is based on the concept of a trivial bundle. Therefore, any system that follows these laws will also be represented as a trivial bundle.
Yes, there are some cases where a Newtonian system may not be represented as a trivial bundle, such as when dealing with non-inertial reference frames or systems with constraints. However, in most cases, a Newtonian system can be mathematically described as a trivial bundle.