lemniscatus

Lemniscatus is a type of closed orbit in mathematics, particularly in the context of celestial mechanics and dynamical systems. This term is used to describe a specific pattern that occurs when a particle or object is subjected to a force that is not radial, meaning it does not point towards the center of the orbit.

The lemniscate of Bernoulli, also known as the lemniscatus, is a specific mathematical curve that is associated with this concept. It is a figure-eight shaped curve that results from a specific combination of algebraic and trigonometric functions. In the context of physics, the lemniscate of Bernoulli represents the boundary beyond which a particle's motion becomes unstable.

In celestial mechanics, the lemniscus is often used as a metaphor to explain the complexity of orbits in terms of force interactions. This concept is also related to the topics of gravitational potential, geodesics, and Lyupanov functions.

Another use of the term "lemniscatus" is in the context of zoology, particularly in relation to a specific genus of an elongated body of shell-bearing mollusks, known as lemniscats or rope shells. These creatures are aquatic and are generally characterized by having a specific rock-like organization of their shells.

The name "lemniscatus" comes from the Latin word for "ribbon" or "zebra-like pattern", and was first used by the 18th-century Swiss mathematician Johann Bernoulli.