Solving Differential - Equation of Motion

In summary, the conversation discusses an equation in the form of a differential equation that describes the motion of a beam. The equation involves variables for position and velocity, and the goal is to solve for these variables as functions of time. One suggestion is to use e^iat style functions, but the speaker is unsure if this applies to their equation. The original equation is later clarified to be equal to 0.
  • #1
aerowenn
19
0
Let's say I have the equation:

##\ddot {\theta}(t)(J + y(t)^2) + 2 \dot {\theta}(t) y(t) \dot y(t) + \ddot y(t)Jn##

It's the general form of an equation I'm working with to describe the motion of a beam. As you can see both ##{\theta}(t)## and y(t) are equations of t. J and Jn are just constants.

I'm wanting to solve for ##{\theta}(t)##, ##\dot {\theta}(t)##, and ##\ddot {\theta}(t)## as a function of time. These will correspond to position, velocity, and acceleration around an axis.

I'm not sure how to go about this (differential) generally, I'm wanting the solutions mentioned about to come out something like:

##{\theta}(t)## = (equation of t)

Any help would be greatly appreciated!
 
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  • #2
have you tried using e^iat style functions for theta(t)?

I ask because its sometimes used when you periodic motion which in your case is rotating about an axis.
 
  • #3
That's not a differential equation. Is one of those "+" signs supposed to be an "=" sign? Or is the whole formula equal to something, say "0"?
 
  • #4
HallsofIvy said:
That's not a differential equation. Is one of those "+" signs supposed to be an "=" sign? Or is the whole formula equal to something, say "0"?

Terribly sorry about that, you are correct. All of that is equal to 0.

As for the other response, I thought of that, but I'm not sure the general solution to second order differential equations applies here. Both functions are dependent on "t".
 
  • #5


As a scientist, my suggestion would be to first identify the type of differential equation you are working with. Is it linear or nonlinear? Is it ordinary or partial? These factors will determine the method you can use to solve the equation.

Once you have identified the type of differential equation, you can then proceed with solving it using various methods such as separation of variables, integrating factors, or using a specific software or computer program.

In this particular case, it seems like you are dealing with an ordinary nonlinear differential equation. Some possible approaches to solving it could be using the method of undetermined coefficients or transforming it into a system of differential equations.

It is also important to note that the solutions for ##{\theta}(t)##, ##\dot {\theta}(t)##, and ##\ddot {\theta}(t)## may not come out as simple equations of t, but rather as functions involving other variables and constants. This is a common occurrence in differential equations and should not be a cause for concern.

In any case, it would be best to consult with a mathematics expert or use a reliable software to solve the equation accurately and efficiently. Good luck with your research!
 

1. What is a differential equation of motion?

A differential equation of motion is a mathematical equation that relates the position, velocity, and acceleration of a moving object. It is a way to describe the motion of an object over time.

2. Why do we need to solve differential equations of motion?

Differential equations of motion allow us to predict the future behavior of moving objects based on their initial conditions and the forces acting on them. This is crucial in fields such as physics, engineering, and astronomy.

3. What are the methods used to solve differential equations of motion?

There are several methods used to solve differential equations of motion, including separation of variables, substitution, and using numerical methods such as Euler's method or Runge-Kutta methods.

4. What are the applications of solving differential equations of motion?

Solving differential equations of motion has a wide range of applications, including predicting the motion of planets and satellites, designing control systems for vehicles and robots, and understanding the behavior of complex systems such as fluid flow and electrical circuits.

5. Are there any real-world limitations to solving differential equations of motion?

While differential equations of motion provide a useful tool for predicting the behavior of moving objects, there are certain limitations. These equations may not accurately model systems with high levels of complexity or non-linear behavior, and they may also be affected by uncertainties in initial conditions or external forces.

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