A simple pendulum can actually be described with rotational motion about the fixed point at the top. Think of a circle of r^2 = x^2 + y^2, r is a fixed length l in this case, and the generalized coordinate theta is used instead of x and y (which can both be determined from any theta and radius, y = l*cos(theta) & x = l*sin(theta) ). The kinetic energy for x and y will then simplify into the rotational kinetic energy. The only difference here is that the radius will be displaced from the original length l over time due to the stretch of the spring, which will be reflected in the kinetic and potential energies as shown above. In the video, v is not the translational velocity, but instead the rate at which the pendulum radius is changing. The point of using theta instead of x and y is to reduce the number of needed equations to describe the system, to 2 instead of 3 in this case.
Bro your lagrangian is correct but the way you have derived it is totally wrong! Why the hell rotational kinetic energy is coming into picture! Just write the translational energy and who get the desired lagrangian I am not saying it's not correct, but rotation of a point is usually not a meaningful concept
Thanks for the video, i finally understand what i took for mistake.
thanks man, this really helped me out!
Excellently explained,TQ
Thank you so much!
Could someone help me understand autoparametric resonance from this?
Why include rotational kinetic energy? Nothing is rotating. This is not included in the equivalent simple pendulum analysis.
A simple pendulum can actually be described with rotational motion about the fixed point at the top. Think of a circle of r^2 = x^2 + y^2, r is a fixed length l in this case, and the generalized coordinate theta is used instead of x and y (which can both be determined from any theta and radius, y = l*cos(theta) & x = l*sin(theta) ). The kinetic energy for x and y will then simplify into the rotational kinetic energy. The only difference here is that the radius will be displaced from the original length l over time due to the stretch of the spring, which will be reflected in the kinetic and potential energies as shown above. In the video, v is not the translational velocity, but instead the rate at which the pendulum radius is changing. The point of using theta instead of x and y is to reduce the number of needed equations to describe the system, to 2 instead of 3 in this case.
@@Coolbeanz9001 exactly
gives the same results even if you decompose translational velocity, but agree his equation for kinetic energy is little odd to understand.
Thanks
Thank u!!!!!!
Bro your lagrangian is correct but the way you have derived it is totally wrong! Why the hell rotational kinetic energy is coming into picture! Just write the translational energy and who get the desired lagrangian
I am not saying it's not correct, but rotation of a point is usually not a meaningful concept