+
+// Here are some generic implementations of a few simple integrators. To use,
+// you need one type representing the state and another containing the
+// derivatives of the primary state variables. The state class must implement
+// these methods:
+//
+// void getDerivative(Derivative_Type& derivative, Scalar absoluteTime);
+// void step(const Derivative_Type& derivative, Scalar deltaTime);
+//
+// Additionally, the derivative class must overload a few operators:
+//
+// Derivative_Type operator+(const Derivative_Type& other) const
+// Derivative_Type operator*(const Derivative_Type& other) const
+
+template<typename S, typename D>
+inline D evaluate(const S& state, Scalar t)
+{
+ D derivative;
+ state.getDerivative(derivative, t);
+ return derivative;
+}
+
+template<typename S, typename D>
+inline D evaluate(S state, Scalar t, Scalar dt, const D& derivative)
+{
+ state.step(derivative, dt);
+ return evaluate<S,D>(state, t + dt);
+}
+
+
+template<typename S, typename D>
+inline void euler(S& state, Scalar t, Scalar dt)
+{
+ D a = evaluate<S,D>(state, t);
+
+ state.step(a, dt);
+}
+
+template<typename S, typename D>
+inline void rk2(S& state, Scalar t, Scalar dt)
+{
+ D a = evaluate<S,D>(state, t);
+ D b = evaluate<S,D>(state, t, dt * SCALAR(0.5), a);
+
+ state.step(b, dt);
+}
+
+template<typename S, typename D>
+inline void rk4(S& state, Scalar t, Scalar dt)
+{
+ D a = evaluate<S,D>(state, t);
+ D b = evaluate<S,D>(state, t, dt * SCALAR(0.5), a);
+ D c = evaluate<S,D>(state, t, dt * SCALAR(0.5), b);
+ D d = evaluate<S,D>(state, t, dt, c);
+
+ state.step((a + (b + c) * SCALAR(2.0) + d) * SCALAR(1.0/6.0), dt);
+}
+
+