Why do we do anything in physics? We do it because it gives a good description of what we can observe.avito009 said:Why do we calculate the lagrangian or hamiltonian?
No, when the action is extremised (i.e., maximised, minimised, or finding a saddle point) we find the equations of motion. The action is the time integral of the Lagrangian.avito009 said:When the Lagrangian is maximised it gives equations of motion.
Both Lagrangian and Hamiltonian are mathematical models used to describe the motion of objects in physics. The main difference between them lies in the way they approach the problem. Lagrangian uses the concept of energy to calculate the motion of objects, while Hamiltonian uses the concept of momentum. In simpler terms, Lagrangian looks at the total energy of an object, while Hamiltonian looks at how the energy is distributed within the object.
Lagrangian and Hamiltonian equations are mathematical equations that describe the motion of objects in a system. These equations take into account factors such as mass, velocity, and potential energy to calculate the position and velocity of an object over time. These equations are commonly used in mechanics, electromagnetism, and quantum mechanics.
Lagrangian and Hamiltonian are used to solve complex problems in physics, such as calculating the motion of celestial bodies, predicting the behavior of particles in quantum mechanics, and understanding the dynamics of mechanical systems. These models provide a more comprehensive and efficient way of analyzing and predicting the behavior of objects in motion.
One of the main benefits of using Lagrangian and Hamiltonian is that they provide a more simplified and elegant approach to solving complex problems in physics. They also take into account all the relevant factors, making the calculations more accurate and efficient. Additionally, these models can be applied to a wide range of physical systems, making them highly versatile and useful in many fields of science and engineering.
No, Lagrangian and Hamiltonian cannot be used interchangeably as they are two different mathematical models with their own specific applications. While they both describe the motion of objects, they use different concepts and approaches to do so. It is important to use the appropriate model depending on the specific problem being solved in order to obtain accurate results.