Revolving around a sphere helically?

  • Thread starter Thread starter ManDay
  • Start date Start date
  • Tags Tags
    Sphere
AI Thread Summary
The discussion centers on the possibility of an entity revolving helically around a sphere while maintaining equal distance from its surface, solely under the influence of a radial force. It is noted that according to Newton's second law, such a motion would not occur, as the entity would only follow a great circle path. The conversation also touches on the mathematical impossibility of having a spring-like motion constrained to a spherical surface. A suggestion is made that if a long, dense cylinder were used as a force source, helical orbits could be achieved, but these would distort near the cylinder's ends. Overall, the feasibility of helical motion on a sphere remains unsubstantiated in traditional physics and mathematics.
ManDay
Messages
157
Reaction score
1
Dumb question maybe, since I'm not a mathematician, but is there something like a specific kind of space in which an entity given a certain initial velocity parallel to the surface of a sphere and constrained to equal distance to the surface of it will revolve arround the square helically (not equatorially), without being exerted any force other than the one running perpendicular to the surface?
 
Mathematics news on Phys.org
ManDay said:
Dumb question maybe, since I'm not a mathematician, but is there something like a specific kind of space in which an entity given a certain initial velocity parallel to the surface of a sphere and constrained to equal distance to the surface of it will revolve arround the square helically (not equatorially), without being exerted any force other than the one running perpendicular to the surface?

Hi ManDay! :smile:

(btw, "helically" means like a spring … did you mean like a sort-of sine function?)

If the only force is radial, then good ol' Newton's second law means that the particle will have no reason to turn, and so will move along a great circle ("an equator").

The radial force may change the speed along that great circle, but can't make it deviate from the great circle. :smile:
 
Like a spring, yes.

Since this is the physics-forum I assume you can assume that everyone can presume at least a basic knowledge. Know about that "Newton-stuff" :D I'm concerning the mathematical aspects since this is the maths-subsection. I was asking for a sort of special topology or reference-space in this would be possible.
 
Last edited:
ManDay said:
Like a spring, yes.

Mathematically, you can't have a spring on the surface of a sphere, or "constrained to equal distance to the surface".
I was asking for a sort of special topology or reference-space in this would be possible.

Changing the coordinates won't alter this basic reality. :redface:
 
If you hand an infinitely-long cylinder of matter as the source of the force, then there would be helical orbits around it.

Consequently, for a finite cylinder, if it is sufficiently long and dense, and you stay near the center (away from the endpoints), then there are orbits which locally look like helices. But since the cylinder is finite, these orbits will distort as they get closer to the endpoints.
 
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
Back
Top