Why no higher derivative in physics?

[swampwiz]

Dear all,

I'm asking why there is no higher derivative than two in physics ? I never encountered a third (time or space) derivative in physics.

Have you some litterature about this?

Thank you.

Regards.

I would say the short answer is that the all phenomena can be represented as a perturbation upon a differential equation having constant coefficients. The solutions of such a differential equation map out to functions that are the exponential functions (i.e., of the natural logarithm base, e) of the input variable scaled by the values that are the root of the polynomial equation that corresponds to the original differential equation such that the order of the differential is the power of the polynomial term (this is standard material covered by a course in differential equations). Now, for a polynomial with real coefficients, the roots must either be real values or pairs of complex conjugate values, and those pairs when multiplied together yield a quadratic factor; hence whatever is modeled mathematically can be resolved down to a function in which is no more than quadratic in nature, and hence, all that is needed to describe it is the use of at most the 2nd differential.

 

[Eric Bretschneider]

The Blasius equation relates to boundary layer flow on along a semi-infinite plate

2f''' + f''f = 0