Information on Impulse Differential Equations

In summary, impulse differential equations have been used in orbital mechanics and have recently gained attention in modeling a zombie takeover. For further resources, the books "Orbital Mechanics: Theory and Applications" by Tom Logsdon and "Differential Equations with Applications to Mathematical Biology" by Paul D. Rabinowitz are recommended. Online resources such as academic journals and specific topic searches can also provide valuable information.
  • #1
Dustinsfl
2,281
5
I read a dumb article on a UK mathematician modeling a zombie take over with impulse differential equations. Unbeknownst to me, were impulse DE and the fact that they are used in orbital mechanics. I am unable to find much on this topic tough. I believe it is relative new (1990).

Does anyone know of any books on impulse DE either related to orbital mechanics or not?

Or does anyone know of any good online resources on the topic?
 
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  • #2


Hello,

As a scientist with a background in mathematics and physics, I find this topic quite interesting. It is true that impulse differential equations have been used in studying orbital mechanics, but their application in modeling a zombie takeover is certainly a unique one.

I would recommend checking out the book "Orbital Mechanics: Theory and Applications" by Tom Logsdon. It covers the basics of orbital mechanics and includes a section on impulse differential equations. Additionally, you can also look into "Differential Equations with Applications to Mathematical Biology" by Paul D. Rabinowitz, which includes a chapter on impulse differential equations in biological systems.

In terms of online resources, I would suggest looking at academic journals such as "Journal of Differential Equations" and "Applied Mathematics and Computation" for articles on impulse differential equations. You can also search for specific topics within the field, such as "impulse differential equations in biological systems" or "impulse differential equations in orbital mechanics."

I hope this helps in your research on impulse differential equations. Best of luck!
 

FAQ: Information on Impulse Differential Equations

What is an impulse differential equation?

An impulse differential equation is a type of differential equation that involves sudden, instantaneous changes in a system. These changes are represented by impulses, which are mathematical functions that have a value of zero everywhere except at one specific point.

How is an impulse differential equation different from a regular differential equation?

The main difference is that an impulse differential equation involves discontinuities, while regular differential equations do not. These discontinuities can make solving the equation more challenging, as they require special techniques such as the Laplace transform or the Dirac delta function.

What are some real-world applications of impulse differential equations?

Impulse differential equations are commonly used in physics, engineering, and other sciences to model systems that experience sudden changes or impacts. Some examples include the motion of a ball bouncing off a surface, the dynamics of a rocket launching, and the behavior of electrical circuits.

Are there any limitations to using impulse differential equations?

Yes, there are some limitations. Impulse differential equations are not always applicable to systems that have continuous changes or are highly nonlinear. They also require initial conditions at the point of the impulse, which may not always be known or measurable in real-world situations.

How can I solve an impulse differential equation?

To solve an impulse differential equation, you can use a variety of techniques such as the Laplace transform, the method of undetermined coefficients, or numerical methods. It's important to carefully consider the initial conditions and understand the nature of the impulse in order to choose the most appropriate method for solving the equation.

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