- #1
grecko94
- 19
- 1
Hello guys, i`m currently making simulation of 2 dimension rolling disk on elastic sin/cosine plane. I`m just wondering if the theory applicable.
I Hertzian contact theory on sin and cosine plane
AI Thread Summary
The discussion centers on simulating a two-dimensional rolling disk on an elastic sine/cosine plane. Participants seek clarification on the definition of a sine/cosine plane to ensure a useful response. The simulation involves a solid disk interacting with an elastic cosine surface. There is confidence expressed in the applicability of Hertz's theory to this scenario. The conversation concludes positively, affirming the theoretical foundation for the simulation.
- #2
Dr.D
- 2,411
- 723
What is a sin/cosine plane? We need a definition/description here before there can be a useful answer.
- #3
grecko94
- 19
- 1
so sorry, i forgot to add the figure
- #4
- #5
Dr.D
- 2,411
- 723
I cannot see any reason to doubt the applicability of Hertz' theory here.
- #6
grecko94
- 19
- 1
its settled then ! thank you 
Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire.
We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges.
By using the Lorenz gauge condition:
$$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$
we find the following retarded solutions to the Maxwell equations
If we assume that...
Maxwell’s equations imply the following wave equation for the electric field
$$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2}
= \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$
I wonder if eqn.##(1)## can be split into the following transverse part
$$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2}
= \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$
and longitudinal part...
Is it true that in any mechanical set-up, it is possible to predict the nature of Normal Reaction ( magnitude, direction, etc. ) without solving through the dynamical equations of motion and constraints for the set-up as Normal Reaction is completely unknown? I mean is it true that we can explain NR intuitively beforehand?
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