Shorter product lifecycles are also leading to even shorter planning times for the development of production systems. In most companies, the restructuring is carried out within a few weeks during the annual holidays. Digital tools such as simulations or the digital twin are used to avoid delaying the restructuring during this time. However, the introduction of a 3D model of the factory is often the first point of failure for many companies. This article proposes a six-step process model that enables the transition from 2D to 3D design. The process model was evaluated in a research project.

We study the Euler–Lagrange flow of a Tonelli Lagrangian on the 2-torus $\mathbb{T}^{2}$ at a fixed energy level ${\mathcal{E}}\subset T\mathbb{T}^{2}$ strictly above Mañé’s strict critical value. We prove that, if for some rational direction ${\it\zeta}\in S^{1}$ there is no invariant graph ${\mathcal{T}}\subset {\mathcal{E}}$ over $\mathbb{T}^{2}$ for the Euler–Lagrange flow with the property that all orbits on ${\mathcal{T}}$ have an asymptotic direction equal to ${\it\zeta}$ , then there are chaotic dynamics in ${\mathcal{E}}$ . This implies that, if the topological entropy of the Euler–Lagrange flow in ${\mathcal{E}}$ vanishes, then in ${\mathcal{E}}$ there are invariant graphs for all asymptotic directions ${\it\zeta}\in S^{1}$ and integrable-like behavior on a large scale.