Set valued force laws

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Mechanics, as one of the oldest natural sciences, plays a crucial role in the development of exact sciences through its relationship with mathematics. Virtually every area of mathematics has applications in mechanics, leading to highly developed theoretical methods across various levels of abstraction. The advent of digital processors has further advanced these methods, enabling their implementation in commercial computer codes. However, in teaching, research, and industry, mechanics transcends mere data production; it encompasses a broad spectrum that includes applied mechanics, analytical and technical mechanics, modeling, experimental mechanics, and technical realization. Key subdisciplines include rigid body mechanics, continuum mechanics, and fluid mechanics. A fundamental concept in nearly all natural sciences is linearization, which relies on the differentiability of mappings. Classical mechanics fundamentally depends on this quality, highlighting the intricate connections between mechanics and other scientific disciplines.