classical-mechanics

In classical mechanics, for an autonomous dynamical system, trajectories in phase space cannot intersect themselves because the state uniquely determines the future evolution (given by a time-...

I'm finishing up my first semester of Classical Mechanics. My professor wrote something to the effect of The main idea behind the Calculus of Variations is given a set of generalised coordinates ...

This is the standard college problem that seems very basic. As shown in the diagram, a car moves up a semi-circular hill. The motion is circular at constant speed. As the car moves up this hill the ...

euok124 - 5 - 1 Im 1st year engineering student (ECE) but im interested in self studying physics. I want to self study taylor classical mechanics this summer preferably including analytic mechanics chapters but i want to know if my math is enough for it. By the end of this year i will have: Partial derivatives. Taylor series. L'hopital. eigenvalues and eigenvectors. Techniques of integration. Def…

In 1687, Sir Isaac Newton published Philosophiæ Naturalis Principia Mathematica , or the Principia , marking a turning point in scientific thought. This monumental work introduced Newton’s three Laws of Motion, which became the foundation of classical mechanics and reshaped our understanding of the physical universe. Newton's First Law, or the Law of Inertia, states that an object will remain at …

Sir Isaac Newton, President of the Royal Society, was an English mathematician, physicist, astronomer, alchemist, and natural philosopher, widely regarded as one of the greatest scientists in history. Born on December 25, 1642, Newton's contributions laid the foundations of classical mechanics and transformed scientific understanding during the Enlightenment. Newton's seminal work, Philosophiae N…

If you missed my previous physics questions to ChatGPT, check them out here and here. In this particular case, I asked ChatGPT a rather common question, and ended up having an argument with it. My questions are in red while ChatGPT's responses are in blue. Three projectiles of the same mass are launched from the top of a cliff with the same initial speed. The first projectile is launched at an an…

Introduction This article follows on from the previous on an alternate approach to solving collision problems. In that article, we determined the equal and opposite collision impulse to have magnitude ##\mu \Delta v## for perfectly inelastic collisions, ##\mu(1+e) \Delta v## for semi-elastic collisions, and ##2\mu \Delta v## for elastic collisions which will be the focus...

Introduction Collisions are very much a stock item in any school physics curriculum and students are generally taught about the use of the principles of conservation of momentum and energy for solving simple collision problems in one dimension. In this article, we will be examining a very common type of collision problem: the inelastic collision....

Here is another version of proof of Maupertuis’s principle. This version is pure Hamiltonian and independent of the Lagrangian approach. The proof is based upon the  Hamiltonian version of the Vector Field Straightening Theorem. It seems that such a style of exposition simplifies the understanding of this non-trivial construction.   First, recall and briefly discuss...

There is an interesting thing in teaching of Classical Mechanics. Several theorems which presented below form a core part of kinematics for all Russian textbooks in Classical Mechanics (excluding Classical Mechanics for physicists)  but European and USA textbooks contain this material just partly and from time to time. Perhaps I just do not know enough...

I've had many posts on here on how physics is applied to sports. This video presents a lecture on the relationship between physics (classical mechanics) and sports/games. It appears that this was given just before last year's London Olympics. Zz.

Each year, during this time of the year in the US, many pumpkins are scarified in the name of physics! :) This is another example of a physics high school teacher trying to demonstrate Newtonian mechanics by shooting pumpkins . “The students got a lot out of the project, but they're not done yet,” said physics teacher Jeff Partynski. “They must now analyze the flight of their pumpkins and creat…

This fall I'm going to be teaching honors introductory mechanics to incoming undergraduates - basically the class that would-be physics majors take.  Typically when we first teach students mechanics, we start from the point of view of forces and Newton's laws, which certainly parallels the historical development of the subject and allows students to build some physical intuition.  Then, in a late…