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A verified method for solving piecewise smooth initial value problems

Ekaterina Auer, Stefan Kiel, Andreas Rauh (2013)

International Journal of Applied Mathematics and Computer Science

In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short overview...

Aerodynamic deceleration at velocities near the escape velocity

Bartoň, Stanislav (2025)

Programs and Algorithms of Numerical Mathematics

This article presents basic procedures for calculating the trajectory of a spaceship that uses only the Earth’s atmosphere to reduce its speed, allowing it to land on the Earth’s surface successfully. The first flight of the ARTEMIS program, which took place from November 16 to December 11 2022, was used as a template for the calculations. All calculations are performed in the symbolic algebra program Maple. To simplify the calculations, forces that have a less significant impact on the shape of...

Algebraic integrability for minimum energy curves

Ivan Yudin, Fátima Silva Leite (2015)

Kybernetika

This paper deals with integrability issues of the Euler-Lagrange equations associated to a variational problem, where the energy function depends on acceleration and drag. Although the motivation came from applications to path planning of underwater robot manipulators, the approach is rather theoretical and the main difficulties result from the fact that the power needed to push an object through a fluid increases as the cube of its speed.

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