Lagrangian Mechanics - Lesson 3: The Brachistochrone Problem

►►►CHECK OUT OUR MOST POPULAR, BEST-SELLING Udemy COURSES: http://udemy.thekaizeneffect.com/ http://relativity.thekaizeneffect.com/ http://explore.thekaizeneffect.com/ ►►►Join our Facebook community to sharpen your mind and interact with others:   / sharpenyourmind   ►►►Book one of our legendary programs and get extra help: http://www.thekaizeneffect.com/Servic... ►►►Donate to support our underlying mission and goals: https://www.paypal.com/cgi-bin/webscr... Lesson Description: ************************************** In this video, we're going to continue our journey in learning the language of Lagrangian Mechanics - which is formally known as Calculus of Variations. In our previous videos, we've derived the Euler-Lagrange equation and discovered how it can be used to minimize functionals, or functions of other functions. Now, we're going to further cultivate familiarity with that equation and its ultimate use. To do that, we're going to solve an age-old problem known as the "Brachistochrone Problem". As its name implies, this problems involves determining the path of shortest time between two points. Such a problem was actually a challenge for many mathematicians back in the day, but we're going to see how calculus of variations makes it almost trivial, at best. By running through this third example utilizing the Euler-Lagrange Equation, you should become fluent in Calculus of Variations. In the next video in this series, we're going to finally put all of this ingenuity to use. I'll go ahead and derive the main equations of Lagrangian Mechanics and show how an understanding of Calculus of Variations plays a pivotal role in doing so. So, stay tuned!! If you need any assistance with this information, feel free to check out our services or send me an email: http://www.thekaizeneffect.com/servic... [email protected] Discussed Topics: **************************************