Explicit Euler Solver

Description

In Sofa, EulerSolver denotes the ODE solver using the explicit integration scheme for the computing of the dynamic system. This integration scheme resolves the system in relation to time: given the mechanical state at time Tn, compute the state at time Tn+1=Tn + dt.
Key points

According to Taylor expansion, the error for the first derivative approximation of a function f(t) is in relation to dt and f"(t). The term f"(t) can represent the dynamic (forces, acceleraion) of the system. Thus, there are two important criteria for stabilization when using the explicit EulerSolver:

In this example, if the time step is set higher (dt=0.001), or by using [Shift + leftmouse] to tug the object in order to dynamically unstabilize the system, the system becomes unstable as showm below :