Posts tagged lagrangian-formalism
A particle is subjected to the potential V (x) = −F x, where F is a constant. The particle travels from x = 0 to x = a in a time interval t0 . Assume the motion of the particle can be expressed i...
$L=T-U$ Here, $L$ is Lagrangian. T is kinetic energy. U is potential energy. But, what Lagrangian actually is? I know what Holonomic and non-holonomic is. But, I was thinking what the Lagrangian re...
$$L'=\frac{m}{2}(a\dot{x}^2+2b\dot{x}{y}+c\dot{y}^2)-\frac{k}{2}(ax^2+2bxy+cy^2)$$where a, b, and c are arbitrary constants but subject to the condition that $b^2 − ac \ne 0$. What are the equat...
How to derive the Lagrangian differential force? $$\frac{d}{dt}(\frac{\partial L}{\partial \dot{x}})+\frac{\partial L}{\partial x}=0$$ I was trying to do something. $$L=T-U=\frac{1}{2} m\dot{x}^...
I have a question about the discussion of constrained Lagrangian systems in the book Mathematical Aspects of Classical and Celestial Mechanics by Arnold et al. (section 1.2.5). The Lagrangian syst...
