Of the two, lateral dynamics has proven to be the more complicated, requiring three-dimensional, multibody dynamic analysis with at least two generalized coordinates to analyze. At a minimum, two coupled, second-order differential equations are required to capture the principal motions.[2] Exact solutions are not possible, and numerical methods must be used instead.[2] Competing theories of how bikes balance can still be found in print and online. On the other hand, as shown in later sections, much longitudinal dynamic analysis can be accomplished simply with planar kinetics and just one coordinate. Three-dimensional space is a geometric 3-parameters model of the physical universe (without considering time) in which we exist. These three dimensions are commonly called length, width, and depth (or height), although any three directions can be chosen, provided that they do not lie in the same plane. In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called 3-dimensional Euclidean space. It is commonly represented by the symbol . This space is only one example of a great variety of spaces in three dimensions called 3-manifolds. In analytical mechanics, specifically the study of the rigid body dynamics of multibody systems, the term generalized coordinates refers to the parameters that describe the configuration of the system relative to some reference configuration. These parameters must uniquely define the configuration of the system relative to the reference configuration.[1] The generalized velocities are the time derivatives of the generalized coordinates of the system. An example of a generalized coordinate is the angle (anti-clockwise from some ref rence point) that locates a point moving on a circle. The adjective "generalized" distinguishes these parameters from the traditional use of the term coordinate to refer to Cartesian coordinates: for example, describing the location of the point on the circle using x and y coordinates. Although there may be many choices for generalized coordinates for a physical system, parameters are usually selected which are convenient for the specification of the configuration of the system and which make the solution of its equations of motion easier. If these parameters are independent of one another, then number of independent generalized coordinates is defined by the number of degrees of freedom of the system. In physics and engineering, kinetics is a term for the branch of classical mechanics that is concerned with the relationship between the motion of bodies and its causes, namely forces and torques.[1][2][3] Since the mid-20th century, the term "dynamics" (or "analytical dynamics") has largely superseded "kinetics" in physics text books;[4] the term "kinetics" is still used in engineering. In mechanics, the Kinetics is deduced from Kinematics by the introduction of the concept of mass. In plasma physics, kinetics refers to the study of continua in velocity space. This is usually in the context of non-thermal (non-Maxwellian) velocity distributions, or processes that perturb thermal distributions.These plasmas cannot be adequately described with fluid equations. Such plasmas are termed kinetic plasmas. The term kinetics is also used to refer to chemical kinetics, particularly in chemical physics and physical chemistry.[5][6][7][8][9] In such uses, a qualifier is often used or implied, for example: "physical kinetics", "crystal growth kinetics", and so on.