Example of Stochastic DE for elementary physics?

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SUMMARY

This discussion focuses on the application of stochastic differential equations (SDEs) to elementary physics problems, specifically in modeling an object sliding down a non-frictionless ramp. The conversation highlights the need for a stochastic model of the friction coefficient, which varies along the ramp's distance. Participants seek tutorials that demonstrate how to define this stochastic process alongside parameters such as the ramp's slope and the object's mass, ultimately aiming to solve for the distance traveled by the object.

PREREQUISITES
  • Understanding of stochastic differential equations (SDEs)
  • Familiarity with basic physics concepts, particularly friction and motion
  • Knowledge of mathematical modeling techniques
  • Experience with numerical simulation tools for solving differential equations
NEXT STEPS
  • Research tutorials on applying stochastic differential equations in physics
  • Explore numerical methods for solving SDEs, such as the Euler-Maruyama method
  • Study the impact of varying friction coefficients in classical mechanics
  • Investigate software tools like MATLAB or Python libraries for simulating stochastic processes
USEFUL FOR

Students and researchers in physics, mathematicians interested in stochastic processes, and educators looking to incorporate advanced modeling techniques into physics curricula.

Stephen Tashi
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Are there any tutorials that apply stochastic differential equations to the settings of elementary physics problems ? - for example, an object sliding down a not-frictionless ramp.

The ramps of everyday life don't have a constant coefficient of friction. A better model for them would be that the friction coefficient is a stochastic process that takes place over the distance of the ramp. An imitation of an elementary physics scenario would be to specify that process as a "given", along with the slope of the ramp and the mass of the object. The task would be to solve for the stochastic process that describes the distance the object has traveled down the ramp..
 

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