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  2. Castigliano's method - Wikipedia

    en.wikipedia.org/wiki/Castigliano's_method

    Castigliano's method for calculating displacements is an application of his second theorem, which states: If the strain energy of a linearly elastic structure can be expressed as a function of generalised force Q i then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement q i in the direction of Q i.

  3. Differential equation - Wikipedia

    en.wikipedia.org/wiki/Differential_equation

    In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. [1] In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two.

  4. Duhamel's principle - Wikipedia

    en.wikipedia.org/wiki/Duhamel's_principle

    (The expression in parentheses is just (,) in the notation of the general method above.) So a solution of the original initial value problem is obtained by starting with a solution to the problem with the same prescribed initial values problem but with zero initial displacement, and adding to that (integrating) the contributions from the added ...

  5. Collocation method - Wikipedia

    en.wikipedia.org/wiki/Collocation_method

    In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...

  6. Fick's laws of diffusion - Wikipedia

    en.wikipedia.org/wiki/Fick's_laws_of_diffusion

    Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...

  7. Displacement (geometry) - Wikipedia

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

    Displacement is the shift in location when an object in motion changes from one position to another. [2] For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity).

  8. Ordinary differential equation - Wikipedia

    en.wikipedia.org/wiki/Ordinary_differential_equation

    In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable.As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. [1]

  9. Displacement - Wikipedia

    en.wikipedia.org/wiki/Displacement

    Displacement (linguistics), the ability of humans (and possibly some animals) to communicate ideas that are remote in time and/or space; Forced displacement, by persecution or violence; Displacement (psychology), a sub-conscious defense mechanism; Displacement (parapsychology), a statistical or qualitative correspondence between targets and ...