स्नातक (प्रारंभिक)Applied Mathematicsनियोजित
Classical mechanics
Newton's laws as differential equations, conservation of energy and momentum, oscillators, central forces and Kepler's laws, and an introduction to Lagrangian mechanics.
math.applied.classical-mechanics
इस विषय का पाठ अभी लिखा नहीं गया है। नीचे दी गई रूपरेखा पाठ्यक्रम-मानचित्र का हिस्सा है और इसकी समीक्षा नहीं हुई है।
इस पर आधारित
38 अनिवार्य पूर्वापेक्षाएँ (बिल्कुल नीचे तक)
आप सीखेंगे
- Solve the equations of motion of projectiles and of harmonic oscillators, with and without damping.
- Use conservation of energy and angular momentum to analyse motion under a central force and derive Kepler's laws.
- Derive equations of motion from a Lagrangian using the Euler–Lagrange equations.
परिभाषा
- Newton's second law: F = ma, where the acceleration a is the second derivative of position.
- A force field F is conservative if F = −∇V for some potential V.
- The Lagrangian of a system is L = T − V, kinetic energy minus potential energy.
प्रमेय
- For conservative forces the total energy T + V is conserved.
- Under a central force, angular momentum is conserved and the motion stays in a plane.
- Bound orbits under an inverse-square attractive force are ellipses (Kepler's first law).
आम भ्रांतियाँ
- Thinking a force is needed to keep an object moving at constant velocity.
- Confusing mass with weight.
वैकल्पिक खोजें
- Smooth manifolds Configuration spaces are manifolds, and Hamiltonian mechanics lives on cotangent bundles with their symplectic structure.
अधिगम पथ
आगे पढ़ने के लिए
- V. I. Arnold, Mathematical Methods of Classical Mechanics
- John R. Taylor, Classical Mechanics (2005)