Trajectories in the context of "Canonical coordinates"

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⭐ Core Definition: Trajectories

A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously.

The mass might be a projectile or a satellite. For example, it can be an orbit — the path of a planet, asteroid, or comet as it travels around a central mass.

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Trajectories in the context of Equifinality

Equifinality is the principle that in open systems a given end state can be reached by many potential means. The term and concept is due to the German Hans Driesch, the developmental biologist, later applied by the Austrian Ludwig von Bertalanffy, the founder of general systems theory, and by William T. Powers, the founder of perceptual control theory. Driesch and von Bertalanffy prefer this term, in contrast to "goal", in describing complex systems' similar or convergent behavior. Powers simply emphasised the flexibility of response, since it emphasizes that the same end state may be achieved via many different paths or trajectories.

In closed systems, a direct cause-and-effect relationship exists between the initial condition and the final state of the system: When a computer's 'on' switch is pushed, the system powers up. Open systems (such as biological and social systems), however, operate quite differently. The idea of equifinality suggests that similar results may be achieved with different initial conditions and in many different ways. This phenomenon has also been referred to as isotelesis (from Greek ἴσος isos "equal" and τέλεσις telesis: "the intelligent direction of effort toward the achievement of an end") when in games involving superrationality.

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