These derivations are simple rearrangement of variables to solve for each variable. Solve for initial velocity (v_0): Solve for final velocity (v): Solve for acceleration (a): Solve for time (t):
read moreThe First Kinematic Equation of Motion is derived from the definition of acceleration, which is the rate of change of velocity with respect to time. If an object starts with an initial velocity v_o, and undergoes a constant acceleration a for a…
read moreThe second law of motion in differential form. This equation is known as the equation of motion, or the second law of motion in differential form. It is a differential equation that describes the relationship between the net force acting on an…
read moreThe total energy of an isolated system remains constant.
read moreThe Equation of Motion in r is a second order differential equation in r. This equation represents a mathematical relationship between the quantities inside the function M, and it states that the value of the function M is zero. The notation of…
read moreAn equation of state is a mathematical relationship that describes the physical properties of a substance, such as its pressure, volume, temperature, and internal energy, in terms of the state variables that characterize its condition. An equation of state typically takes the…
read moreA dynamical system is a mathematical concept used to describe how a set of variables changes over time. In particular, it is a system where the state of the system at any given time determines its future behavior. In a dynamical system,…
read moreAt any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometrical manifold. The evolution rule of the…
read moreA state variable is one of the set of variables that are used to describe the mathematical “state” of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behavior in the absence of…
read moreIn physics, the state of a system refers to a complete description of all the physical properties that are relevant to the behavior of that system. The state of a system can include a wide range of parameters, such as the position…
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