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 Mar 12 answered Rate at which a pendulum bob slows due to air resistance? Mar 10 comment Rate at which a pendulum bob slows due to air resistance? @vincemathic: There are at least two factors that slow the motion: air resistance (fluid friction) and friction in the pendulum axle (dry friction), see link. Fluid friction is proportional to velocity $\sim \dot{\theta}$ (the Stokes' law), while dry friction is described differently. So, you need to be sure that fluid friction is the main dissipation effect. In this case the motion equation is: $\ddot{\theta} + \gamma \dot{\theta} + \omega^2 \sin \theta = 0$ with $\theta(0) = \cos^{-1}((l-h_0)/l)$ and $\dot{\theta}(0)=0$. Mar 10 comment Deeper principles in classical mechanics A book by L.D.Landau and E.M.Lifshits, "Mechanics" (Course of Theoretical Physics, v.1) is a good source for this subject. Using the Hamiltonian formualtion of mechanics, on can derive the conservation laws. May 3 answered What is a physical example of a Saddle-Node Bifurcation? May 1 answered Lagrangian density for a Piano String May 1 awarded Informed May 1 comment sine-Gordon equation Sorry I could not get the book by Rider. But I don't think there is a strict relation between SG and $\phi^4$ models. For example, one can write that $\sin(x) \approx x - x^3/6$, but this does not prove that sinus function is related to a cubic function. BTW, if you take the derivative of your solutions, then eq.(1) gives hyperbolic secant squared, and eq.(2) gives just hyperbolic secant. In this sense, these solutions are related to each other. But in general, the SG model and $\phi^4$ do not have relation in a strict sense. May 1 answered Valid theory in all dimensions for solitary waves Apr 30 awarded Teacher Apr 30 answered sine-Gordon equation Apr 27 answered What is a nonlinear field?