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b888944ab233neighbour

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			********
			Dynamics
			********

			Time discretisation
			===================

			Verlet
			------

			.. code-block:: cpp

			while ( ... )
			{
			// variables & history

			xt::xtensor<double,2> u;
			xt::xtensor<double,1> V;
			xt::xtensor<double,1> A;
			xt::xtensor<double,1> V_n = g.dofs_v();
			xt::xtensor<double,1> A_n = g.dofs_a();

			// new displacement

			xt::noalias(u) = g.u() + dt * g.v() + 0.5 * std::pow(dt,2.) * g.a();

			g.set_u(u);

			// new acceleration

			xt::noalias(A) = g.solve_A();

			g.set_a(A);

			// new velocity

			xt::noalias(V) = V_n + .5 * dt * ( A_n + A );

			g.set_v(V);
			}

			Velocity Verlet
			---------------

			.. code-block:: cpp

			while ( ... )
			{
			// variables & history

			xt::xtensor<double,2> u;
			xt::xtensor<double,1> V;
			xt::xtensor<double,1> A;
			xt::xtensor<double,1> V_n = g.dofs_v();
			xt::xtensor<double,1> A_n = g.dofs_a();

			// new displacement

			xt::noalias(u) = g.u() + dt * g.v() + 0.5 * std::pow(dt,2.) * g.a();

			g.set_u(u);

			// estimate new velocity

			xt::noalias(V) = V_n + dt * A_n;

			g.set_v(V);

			xt::noalias(A) = g.solve_A();

			xt::noalias(V) = V_n + .5 * dt * ( A_n + A );

			g.set_v(V);

			// new velocity

			xt::noalias(A) = g.solve_A();

			xt::noalias(V) = V_n + .5 * dt * ( A_n + A );

			g.set_v(V);

			// new acceleration

			xt::noalias(A) = g.solve_A();

			g.set_a(A);
			}

			Forward Euler
			-------------

			.. code-block:: cpp

			while ( ... )
			{
			xt::noalias(U) = g.dofs_u() + dt * g.solve_V();

			g.set_u(U);
			}