An optimal control approach to the problem of the longest self-supporting structure
- 1. Gran Sasso Science Institute
- 2. Gran Sasso Science Institute, DISIM, Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, Via Vetoio - 67100 L'Aquila, Italy
Description
The characterisation of the self-supporting slender structure with the furthest length is of interest both from a mechanical and biological point of view. Indeed, from a mechanical perspective, this classical problem was developed and studied with different methods, for example using similarity solutions and stable manifolds. However, none of them led to a complete analytical solution. On the other hand, plant structures such as tree branches or searcher shoots in climbing plants can be considered elastic cantilevered beams. In this paper, we formulate the problem as a non-convex optimisation problem with mixed state constraints. The problem is solved by analyzing the corresponding relaxation. With this method, it is possible to obtain an analytical characterization of the cross-section
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