Second Order System

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### Second Order System

##### Description

The Second Order System concept models the algorithmic implementation of the rhs for steppers requirering the second order derivative, hence the r.h.s. of the ODE x'' = f(x,x',t). The only requirement for this concept is that it should be callable with a specific parameter syntax (see below). A Second Order System is typically implemented as a function or a functor. Systems fulfilling this concept are required by the Velocity Verlet method.

##### Notation

`System`

  A type that is a model of Second Order System

`Space`

  A type representing the state x of the ODE

`Velocity`

  A type representing the derivative x' of the ODE

`Acceleration`

  A type representing the second order derivative x'' of the ODE

`Time`

  A type representing the time

`sys`

  An object of type `System`

`x`

  Object of type `Space`

`v`

  Object of type `Velocity`

`a`

  Object of type `Acceleration`

`t`

  Object of type `Time`

##### Valid expressions

Name | Expression | Type | Semantics
--- | --- | --- | ---
Calculate x'' := f(x,x',t) | `sys( x , v , a , t )` | `void` | Calculates f(x,x',t), the result is stored into a.