4.1: Dynamics and motion
Motion is all around you, the universe is full of moving matter and objects. This motion is surprisingly predictable and can therefore accurately be described by laws: Newton’s laws of motion. The field of science and engineering studying the time-dependent motion of matter in the presence of forces is called dynamics. During several centuries dynamical models have been developed that enable scientists to understand many time-dependent processes in nature and have allowed engineers to use this understanding to design and control motion to an extremely high degree. Examples include precise robots, fast formula one racing cars and remotely controlled spacecrafts, all of which have been designed by engineers by applying the concepts that are introduced in this textbook. And who knows? Maybe you will design the next generation of dynamic machines and devices in the future.
Since the early history of mankind people have been studying motion. Astronomers in ancient times were observing the trajectories of celestial objects like moons and planets. Also, motion of objects on earth were being studied, like in the experiment in 1586 where Simon Stevin dropped two balls with different mass from the Nieuwe Kerk in Delft, providing evidence that they fall at the same rate. In 1687 Newton introduced the famous laws of motion in his Principia, which were based on the mathematics he had developed with Leibniz for solving differential and integral equations.
Newton’s laws, which are the building blocks for the field of dynamics, provide a mathematical model to describe the experimentally observed motion of objects in our universe, which is accurate to a very high degree. Deviations from the model occur only in the case where speeds become comparable to the speed of light, such that Einstein’s theory of relativity is needed or if sizes and energies and masses become very small, such that quantum mechanical effects start to play a role. These exceptions, which were only discovered in the \(20^{\text {th }}\) century, belong to the field of modern physics and are outside the scope
of this course, which focuses on classical mechanics and dynamics. In this textbook we will discuss the theoretical models of dynamics based on Newton’s laws as if they represent a perfect description of experimental observations. Nevertheless, it remains important to realise that there is a difference between these models and the experimental observations they attempt to describe, since despite the high degree of accuracy of current physical models, there are still experiments that cannot be captured by them and are subject of thorough scientific investigations. For instance the model for describing the dynamics of stars rotating around the centre of a galaxy is still debated (gravity rotation problem) and the dynamics of particles that were observed to travel upstream into a small waterfall still remains to be explained. See also https:
//en.Wikipedia.org/wiki/List_of_unsolved_problems_in_physics
.
We note here that Newton’s laws are not the only way to describe the experimentally observed motion of objects. Alternative popular formulations of dynamics are Lagrangian and Hamiltonian mechanics, which are dealt with in more advanced textbooks in dynamics. These formulations, yield completely identical results as Newton’s laws, but can in some cases be advantageous to simplify the mathematical analysis.