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captain
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are lagrangians based on physical observation or mathematical reasoning?
I am not sure what you are driving at when you say "it just works out".PhysiSmo said:In the same question, "Why do we use THIS Lagrangian, or THAT, and HOW did we derive it?", I have been told that "it just suits the corresponding problem, it just works out!".
A Lagrangian is a mathematical function that describes the dynamics of a physical system. It is based on the principle of least action, which states that a system will follow the path that minimizes its action, or the integral of its Lagrangian over time.
Lagrangians are used in physics to describe the behavior of systems in classical mechanics, quantum mechanics, and field theory. They provide a more elegant and efficient way to describe the dynamics of a system compared to other methods such as Newton's laws of motion.
Lagrangians are based on both physical observation and mathematics. They are derived from the laws of physics and are used to describe the behavior of physical systems. However, they are also mathematical constructs that use equations and symbols to describe the dynamics of a system.
Lagrangians and Hamiltonians are two different mathematical formulations used to describe the dynamics of a system. While Lagrangians are based on the principle of least action, Hamiltonians are based on the principle of least energy. The equations and variables used in each formulation also differ.
In theory, Lagrangians can be used to describe any physical system. However, in practice, different types of Lagrangians are used for different types of systems, such as classical mechanics, quantum mechanics, and field theory. Some systems may also be too complex to be accurately described by a Lagrangian.