Here is the fifty-sixth episode of Quantum Foam, Mechanics. This is an idea that describes how something works. There is a lot of physics that describes mechanics. This subject is built on top of the ability to do differential equations. Calculus is used on either side of the equation and it is balanced out. We are interested in Differential Equations, Mechanics, and Computation. This idea provides a conceptual introduction to the theory of Ordinary Differential Equations. This covers differential equations and their solutions, second-order ODE and the calculus of variations, Newtonian Mechanics, Numerical Methods, Linear Algebra and analysis, and the magic of iteration. Iterative interpolation is a mathematical method that involves repeatedly refining an approximation of a function or data set by applying interpolation techniques on progressively smaller intervals or domains. This approach helps improve the accuracy of the approximation with each iteration. There are conservation laws. This states that the total energy, momentum, and angular momentum remain constant in an isolated system. There are force laws that describe different pushes and pulls. There is analytical mechanics like Lagrangian and Hamiltonian mechanics. We use the type of physics that we need for each specific problem. For the most part, we have computers that are fast enough to do our math. There are a few areas where our linear computers are unable to calculate the results. There are different places online where this subject can be taught. Space, time, mass, force, momentum, torque, and angular momentum are introduced in classical mechanics. This helped to solve 1 of the most famous physics problems, the motion of the planets. We have vectors, kinematics, Newton's laws, circular motion, drag forces, constraints, continuous systems, momentum and impulse, continuous mass transfer, kinetic energy and work, potential energy and energy conservation, collision theory, rotational motion, angular momentum, rotations and translation, and rolling. Classical mechanics works best for macroscopic objects such as things you can see with the naked eye moving at speeds much slower than the speed of light. There is circular motion, position and velocity, uniform circular motion, circular motion and acceleration, Newton's second law and how that applies to circular motion, angular position and acceleration, pulleys and constraints, resistive forces, 2 blocks and 2 pulleys, conservation of momentum, center of mass and motion of the center of mass, the center of mass of 3 objects, center of mass of a unified rod, relative velocity and recoil, continuous mass transfer, kinetic energy and work in 1D, kinetic energy and work in 2D and 3D, conservative and non-conservative forces, potential energy, conservation of energy, collision theory, motion of a ridged body, moment of inertia, angular momentum of a point particle, torque and angular impulse, gyroscopes, dynamics and vibrations, interference from data and models, electronic and mechanical properties of materials, classical mechanics, dynamics, wave-propagation, electromechanical dynamics, non-linear dynamics, chaos, introduction to oscillations and waves, applied quantum and statistical physics, introduction to statistical physics, mechanical behavior of materials, thermodynamics, kinetics, non-equilibrium statistical mechanics, statistical physics, Nano mechanics of materials, and biomaterials. That is a tentative list on what could be included in mechanics. Machines are designed by us and they are mechanical contraptions. We will use computational ideas to formulate the principles of mechanics precisely. This is where we need differential equations.
