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  2. Fourth, fifth, and sixth derivatives of position - Wikipedia

    en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth...

    Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.

  3. Equations of motion - Wikipedia

    en.wikipedia.org/wiki/Equations_of_motion

    They are often referred to as the SUVAT equations, where "SUVAT" is an acronym from the variables: s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time. [ 10 ] [ 11 ] In these variables, the equations of motion would be written

  4. Action-angle coordinates - Wikipedia

    en.wikipedia.org/wiki/Action-angle_coordinates

    Action angles result from a type-2 canonical transformation where the generating function is Hamilton's characteristic function (not Hamilton's principal function ).Since the original Hamiltonian does not depend on time explicitly, the new Hamiltonian (,) is merely the old Hamiltonian (,) expressed in terms of the new canonical coordinates, which we denote as (the action angles, which are the ...

  5. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to ...

  6. TK Solver - Wikipedia

    en.wikipedia.org/wiki/TK_Solver

    Konopasek's goal in inventing the TK Solver concept was to create a problem solving environment in which a given mathematical model built to solve a specific problem could be used to solve related problems (with a redistribution of input and output variables) with minimal or no additional programming required: once a user enters an equation, TK ...

  7. Displacement (geometry) - Wikipedia

    en.wikipedia.org/wiki/Displacement_(geometry)

    In considering motions of objects over time, the instantaneous velocity of the object is the rate of change of the displacement as a function of time. The instantaneous speed, then, is distinct from velocity, or the time rate of change of the distance travelled along a specific path. The velocity may be equivalently defined as the time rate of ...

  8. Adaptive step size - Wikipedia

    en.wikipedia.org/wiki/Adaptive_step_size

    where y and f may denote vectors (in which case this equation represents a system of coupled ODEs in several variables). We are given the function f(t,y) and the initial conditions (a, y a), and we are interested in finding the solution at t = b. Let y(b) denote the exact solution at b, and let y b denote the solution that we compute.

  9. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    In the simple case of a function of one variable, say, h(x), we can solve an equation of the form h(x) = c for some constant c by considering what is known as the inverse function of h. Given a function h : A → B, the inverse function, denoted h −1 and defined as h −1 : B → A, is a function such that