Why are physics equations second order?

The reason for equations of physics, being of at most second order, is due to the so-called Ostrogradskian instability. (see paper by Woodard). This is a theorem, which states that equations of motion with higher-order derivatives are in principle unstable or non-local.

Does differential equations help with physics?

Differential equations involve the differential of a quantity: how rapidly that quantity changes with respect to change in another. (And, by the time you meet difficult equations in second and higher year physics courses, you will have done more formal study of differential calculus in your mathematics subjects.)

What is second order in physics?

Second-order in time means two derivatives with respect to time. The classic example is the basic one-dimensional wave equation: ∂2ϕ∂t2=∂2ϕ∂x2 . This equation does have time-reversal symmetry, because if you replace t with −t, you get the exact same equation back.

What is the nature of second order wave equation?

Find the nature of the second-order wave equation. The general equation is in this form. Comparing \frac{\partial ^2 u}{\partial t^2}-c^2\frac{\partial ^2 u}{\partial x^2}=0 with the above equation, (let ‘y’ be ‘t’). As d is positive, the second order wave equation is hyperbolic.

Why do we use differential equations in physics?

A differential equation states how a rate of change (a “differential”) in one variable is related to other variables. For instance, when the position is zero (ie. the string is very much stretched or compressed) then the rate of change of the velocity is large, because the spring is exerting a lot of force.

Why does a 2nd order differential equation have two solutions?

5 Answers. second order linear differential equation needs two linearly independent solutions so that it has a solution for any initial condition, say, y(0)=a,y′(0)=b for arbitrary a,b. from a mechanical point of view the position and the velocity can be prescribed independently.

Do all differential equations have infinite solutions?

Given these examples can you come up with any other solutions to the differential equation? There are in fact an infinite number of solutions to this differential equation.

Why are all important differential equations in physics second-order?

First of all, it’s not true that all important differential equations in physics are second-order. The Dirac equation is first-order. The number of derivatives in the equations is equal to the number of derivatives in the corresponding relevant term of the Lagrangian.

What are second order linear equations?

In this chapter we will study ordinary differential equations of the standard form below, known as the second order linear equations: y″ + p(t)y′ + q(t)y= g(t). Homogeneous Equations: If g(t) = 0, then the equation above becomes y″ + p(t)y′ + q(t)y= 0. It is called a homogeneousequation. Otherwise, the equation is

How do you find the general solution of a second order equation?

Fact: The general solution of a second order equation contains two arbitrary constants / coefficients. To find a particular solution, therefore, requires two initial values. The initial conditions for a second order equation will appear in the form: y(t0) = y0, and y′(t0) = y′0.