Brachistochrone curve #physics

The brachistochrone curve is the curve of fastest descent between two points, not the shortest distance. The term “brachistochrone” comes from the Greek words “brachistos” (shortest) and “chronos” (time). In this problem, one needs to find the path along which a particle will slide from one point to another in the shortest time, assuming it moves only under the influence of gravity and without friction. Interestingly, the brachistochrone curve is a cycloid, which is the path traced by a point on the rim of a wheel as it rolls along a straight line. The solution to the brachistochrone problem was first posed by Johann Bernoulli in 1696 and was a major milestone in the development of calculus of variations. Key properties: • The curve is steeper near the start, allowing for a rapid initial gain in speed due to gravity. • It gradually flattens out as the particle approaches the end, ensuring a fast overall travel time. The brachistochrone curve is crucial in various fields like physics and engineering, particularly in problems involving optimal paths or minimal time trajectories. Copyright Disclaimer under section 107 of the Copyright Act of 1976, allowance is made for “fair use” for purposes such as criticism, comment, news reporting, teaching, scholarship, education and research. Fair use is a use permitted by copyright statute that might otherwise be infringing.” Follow us: whatsapp Channel : Telegram Channel : Twitter : Facebook : Instagram: