What Equation Combines Laplacian and Time Derivatives of a Vector Function?

  • Context: Graduate 
  • Thread starter Thread starter Schreiberdk
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around identifying an equation that combines the Laplacian and time derivatives of a vector function. The context includes potential physical applications and interpretations of the equation, particularly in relation to wave phenomena and friction.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents an equation involving the Laplacian of a vector function and its time derivatives, suggesting it equals zero.
  • Another participant proposes that the equation represents the Newton equation for small displacements of a string or membrane, considering friction.
  • A subsequent reply questions whether the equation can be interpreted as a wave equation that accounts for friction.
  • A later response acknowledges a misunderstanding regarding the sign of the Laplacian in the initial equation.

Areas of Agreement / Disagreement

Participants express differing interpretations of the equation's meaning and applications, indicating that the discussion remains unresolved regarding its precise characterization and implications.

Contextual Notes

There are indications of missing assumptions related to the physical context of the equation, as well as potential dependencies on definitions of terms like "friction" and "wave equation." The discussion also highlights an unresolved issue regarding the sign of the Laplacian.

Schreiberdk
Messages
93
Reaction score
0
Hi PF

I need help with identifying an equation. It contains the following:

The sum of: The laplacian of a vectorfunction, the second time derivative of a vectorfunction and the first time derivative of a vectorfunction, which is all equal to zero.

Laplacian(V)+d^2/dt^2(V)+d/dt(V)=0

Anyone got any suggestions, of which equation this might look like, or any specific physical uses of the equation?
 
Physics news on Phys.org
It is the Newton equation for the small displacement of a string (or membrane, etc.) considering friction.
 
Last edited:
So it is a wave equation taking friction into account?
 
Indeed.---EDIT---

Err, not quite. I hadn't noticed the sign of the Laplacian.
 

Similar threads

Graduate Show positivity and boundedness of a non-linear system
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Solution to an ODE (Leaky Integrate and Fire Neuron Model)
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Numerically solving a transport equation
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Crank-Nicholson method for spherical diffusion
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Function differentiability and diffusion
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Explanation of all "its linearly independent derivatives"
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Treating Velocity as Independent of position till the end in Lagrangian Mechanics
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad What are the applications of inverses of vector functions?
  • · Replies 17 ·
Replies
17
Views
3K
Graduate Conceptual trouble with derivatives with respect to Arc Length
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Solving Special Function Equations Using Lie Symmetries
  • · Replies 6 ·
Replies
6
Views
3K