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Ahmad Kishki
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Recommend an easy going introduction to lagrangian and hamiltonian mechanics (for self study)
I liked "Classical Dynamics of Particles and Systems" by Marion and Thornton (advanced undergraduate classical mechanics)Ahmad Kishki said:Recommend an easy going introduction to lagrangian and hamiltonian mechanics (for self study)
I liked "Classical Dynamics of Particles and Systems" by Marion and Thornton (advanced undergraduate classical mechanics)
Lagrangian and Hamiltonian mechanics are two different approaches to studying the motion of particles and systems. Lagrangian mechanics uses the concept of generalized coordinates and the principle of least action to describe the dynamics of a system, while Hamiltonian mechanics uses generalized coordinates and momenta to describe the system's evolution over time. In other words, Lagrangian mechanics focuses on energy conservation, while Hamiltonian mechanics focuses on momentum conservation.
The Lagrangian and Hamiltonian functions are central to the equations of motion in their respective theories. They are both derived from the system's potential and kinetic energy and represent the system's total energy. The Lagrangian function is used to derive the equations of motion in Lagrangian mechanics, while the Hamiltonian function is used to derive the equations of motion in Hamiltonian mechanics.
Yes, Lagrangian and Hamiltonian mechanics are general theories that can be applied to any physical system, as long as the system has a well-defined potential energy function. These theories have been successfully applied to a wide range of systems, from simple particles to complex systems like planets and molecules.
One advantage of using Lagrangian or Hamiltonian mechanics is that they provide a more elegant and concise way of describing the motion of a system. They also offer a deeper understanding of the underlying physical principles governing the system's behavior. Additionally, these theories can handle more complex systems that may be difficult to analyze using Newtonian mechanics.
Yes, there are many real-life applications of Lagrangian and Hamiltonian mechanics. For example, they are used in the analysis of mechanical systems like pendulums, springs, and rigid bodies. They are also used in the study of celestial mechanics, such as the motion of planets and satellites. Additionally, these theories have applications in quantum mechanics, fluid dynamics, and many other areas of physics and engineering.