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Background This textbook is an introduction to and exploration of a number of core topics in the field of applied mechanics. Mechanics, in both its theoretical and applied contexts, is, like all scientific endeavors, a human construct. It reflects the personalities, thoughts, errors, and successes of its creators.
We therefore provide some personal information about each of these individuals when their names arise for the first time in this book. This does not mean that we are writing history. Nevertheless, some remarks putting individuals and ideas in context are necessary in order to make clear what we are speaking about — and what we are not speaking about.
At the end of the 19th century, technical universities were established everywhere in Europe in an almost euphoric manner. But the practice of technical mechanics itself, as one of the basics of technical development, was in a desolate state, due largely to the refusal of its practitioners to recognize the influence of kinetics on motion.
They were correct to the extend that then current mechanical systems moved with small velocities where kinetics does not play a significant role. But they had failed to keep up with developments in the science underlying their craft and were unable to keep pace with the speeds of such systems as the steam engine.
Into this critical situation, Karl Heun introduced a significant, and shortly to become famous, paper about pages in length on the kinetic problems in scientific engineering K.
Through the influence of the renowned mathematician Felix Klein, Heun attained a professorship in Karlsruhe Germany M. Georg Hamel became his assistant, working for him from tillduring which time period he published his habilitation thesis G.
It was due to Felix 1 2 1 Introduction Klein that outstanding scientists like these could eventually bring engineering and natural science back together. Hamel, ] as the work of a contemporarian of that time, or, predating him, the works of J.
No one less an an authority than Louis Poinsot found its historical part outstanding I. Or, for a look backwards from a contemporary viewpoint, one may consult the thoughtful contributions of John Papastavridis, e.
Physics itself, during the nineteenth century, underwent an abstraction process. Following in the footsteps of Ludwig Boltzmann L. Boltzmann,physicists turned to the construction of equations or systems of equations that allowed one to calculate real phenomena without any interpretation of the physical reality.
According to Gustav Kirchhoff, the equation itself is the explanation. However, in mechanics, such a process is extremely dangerous. For example, constraint forces that do not contribute to motion may never be perceived, which can lead to severe misinterpretations.
We will therefore not renounce interpretability as one of the basic concepts in applied mechanics. Pulte cites eminent witnesses for corroboration: Jacobi, and L. However, Jacobi tried to find a mathematical proof for a mechanical principle and Poinsot attempted to deal with scientific falsehoods.
Newton and contemporarians were not able to solve practical problems in mechanics; its basics had not yet been laid.
Moreover, we need the momentum theorem in a calculable form, the breakthrough for which came with Leonhard Euler and his textbook mechanica sive motus scientia anayticae exposita mechanics, or the science of motion, analytically represented from This concept, although insufficient, is often used even today2.
Euler here enlarges his conception to systems of point masses, including liquids K. Simonyi,and, for a rigid body, he derives the momentum of momentum theorem. But he obviously feels that something is missing in his concept. Thus, inhe publishes his famous nova methodus motum corporum rigidorum determinandi new method to determine rigid body motions.
Here, thirty nine years after his first textbook, we find an axiomatic basis of mechanics: These are, till today, as modern as can be. Until then, according to Kurt Magnus3it had been a question of individual taste, or personal training, which method was selected for the derivation of motion equations.
The reason for this statement is, of course, that a calculation by hand allows for a limited number of degrees of freedom only. Here, the choice of method gains in importance.
Karl Heun, with his paper fromhad focused attention on the analytical methods. Gustav Hamel enlarged this concept the Lagrangean equations of the second kind to non-holonomic systems. Szabo, aK.
Simonyi,H. One avoids thus any difficulty with the one weighty but seldom articulated axiom that those principles one has swindled out of particle dynamics are now also applicable to continua.Chapter 4 considers rigid multibody systems The rigid body is thereby defined such that, by relaxation of the rigidity constraints, one can later directly proceed to elastic bodies.
The Central Equation yields a methodology from which the Projection Equation is selected for the derivation of motion equations. Neither of these approaches properly handles both the dynamics of the musculotendons and the complex routing constraints.
We present a new, strand-based approach, capable of handling the coupled dynamics of muscles, tendons, and bones through various types of routing constraints. Publications Search by Program Search Result The search results on this publication page are automated on a monthly schedule based on acknowledgement of NIH Common Fund award numbers and intramural awards.
Therefore, this list is not an exhaustive or error . A Comparison of Two Approaches of Handling Contacts in Rigid Multibody Dynamics Abstract This paper is based on my work completed during an eight-week . A non-smooth contact dynamic approach has been implemented to analyze masonry blocks under dry friction.
• Relying upon the theory of measure differential inclusion, the problem is set as a cone complementary problem. ODE splits the collision handling into two separate parts, the collision detection and the collision handling.
To accelerate the collision detection, it is split up into two phases. First, it is tested if the axis-aligned bounding boxes (AABB) of the geometries under consideration overlap (broad phase).