...one of the most highly
regarded and expertly designed C++ library projects in the
world.
— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards
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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.
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
Name 
Expression 
Type 
Semantics 

Calculate x'' := f(x,x',t) 


Calculates f(x,x',t), the result is stored into a. 