What are these equations representing?

  • Thread starter optics.tech
  • Start date
In summary, these equations may be related to rotational dynamics, harmonic oscillation, or a specific geometry. They were presented in a context of kinematics.
  • #1
optics.tech
79
1
Does anyone know what equations are these (please see attached image)?

Also, does anyone know these complete equations?

Thank you
 

Attachments

  • untitled.PNG
    untitled.PNG
    22 KB · Views: 409
Engineering news on Phys.org
  • #2
They look like they could be related to rotational dynamics, as terms for angular speed ( [tex]\omega[/tex] ) radius ( [tex]r[/tex] ) and time ( [tex]t[/tex] ) are in them. It's also possible they are related to some form of harmonic oscillation, based on the [tex]sin(\omega t)[/tex] terms I see in there.

However they look like they are probably based a specific geometry, as they don't look generalized to me. Where did you see these equations, and what was the context of their presentation?
 
Last edited:
  • #3
The lambda [tex] \Lambda [/tex] and what Mech_ said makes me think they rotordynamic oriented as well.
 
  • #4
The r/L term is usually a slenderness ratio in shaft dynamics. I'll have to look through my rotor dynamics handbook. I agree with Mech in that I bet this is a derivation for a specific condition/geometry. It definitely is taking me back to the days of harmonic functions and Fourier transforms...
 
  • #5
FredGarvin said:
The r/L term is usually a slenderness ratio in shaft dynamics.

I don't disagree with this, but on the far right of the photo it looks like L is the length of a bar connected to a rotating radial link with length r. That would make

[tex]\sqrt{L^2-r^2\sin^2\omega t}=L\sqrt{1-\left(\frac{r}{L}\sin\omega t\right)^2}[/tex],

which appears in one of the equations, the y coordinate of the end of the bar.
 
  • #6
However they look like they are probably based a specific geometry, as they don't look generalized to me. Where did you see these equations, and what was the context of their presentation?

How do you know that the equation is dedicated to specific geometry?

If so, what kind of geometry is it? 2 or 3 dimensional?
 
  • #7
Mapes said:
I don't disagree with this, but on the far right of the photo it looks like L is the length of a bar connected to a rotating radial link with length r. That would make

[tex]\sqrt{L^2-r^2\sin^2\omega t}=L\sqrt{1-\left(\frac{r}{L}\sin\omega t\right)^2}[/tex],

which appears in one of the equations, the y coordinate of the end of the bar.
I think you're right on that. I saw the "a" on the circumference of the circle and thought that r may be the radius of the bar with length L. Your slant is more probable. I wonder if it's just a kinematics equation for a linkage, like you mentioned...
 

1. What is an equation?

An equation is a mathematical statement that shows the relationship between two or more quantities. It typically includes variables, constants, and mathematical operations.

2. How do you solve an equation?

To solve an equation, you need to isolate the variable on one side of the equation by using inverse operations. This means performing the opposite operation on both sides of the equation until the variable is alone on one side.

3. What is the difference between an equation and an expression?

An equation is a mathematical statement that shows equality between two quantities, while an expression is a combination of numbers, variables, and mathematical operations. In other words, an equation has an equal sign, while an expression does not.

4. What are the most common types of equations?

The most common types of equations are linear equations, quadratic equations, and exponential equations. Other types include polynomial equations, logarithmic equations, and trigonometric equations.

5. How do equations relate to real-world problems?

Equations are used to model and solve real-world problems in various fields such as physics, engineering, economics, and chemistry. They help us understand and predict how different quantities are related and how they change over time.

Similar threads

  • Mechanical Engineering
Replies
1
Views
621
  • Mechanical Engineering
Replies
15
Views
853
  • Mechanical Engineering
Replies
33
Views
2K
  • Mechanical Engineering
Replies
1
Views
780
  • Mechanical Engineering
Replies
13
Views
1K
Replies
2
Views
2K
  • Mechanical Engineering
Replies
1
Views
2K
Replies
3
Views
1K
  • Mechanical Engineering
Replies
0
Views
163
  • Mechanical Engineering
Replies
2
Views
2K
Back
Top