Need a real life example where a partial derivative is used in motion

Click For Summary
Partial derivatives are crucial in analyzing motion, particularly in applications like car acceleration and projectile motion. The discussion highlights the importance of considering changes in both velocity and mass, especially in contexts like rocket flight. It emphasizes the use of rotating coordinate systems to simplify the analysis of forces acting on an airplane, such as engine thrust, gravity, and aerodynamic forces. The equations of motion in six degrees of freedom (6-DOF EOM) also involve numerous partial derivatives. Participants are encouraged to explore these equations further and seek clarification as needed.
nrsakinh
Messages
1
Reaction score
0
Homework Statement
I have to find a real life application of partial derivative and have chosen the topic "Motion". I need examples of where the partial derivative is used to calculate speed/acceleration or in projectile motion.
Relevant Equations
-
my group is preferring the ue of partial derivative to find the acceleration of a car or the projectile motion of something being launched
 
Physics news on Phys.org
Have you heard of the Schrodinger equation?
 
Rocket flight. You have to consider both the change in velocity and the change in mass.
 
That is a very good example. Consider a flying airplane. several forces are easiest to consider in different coordinate systems that are rotating with respect to each other. Engine forces line up with the aircraft fuselage. Gravity always lines up in locally level Earth coordinates. Aerodynamics forces line up with the relative air flow. Those are all rotating with respect to each other, so there are partial derivatives all over the place.

But even without considering that, looking at one rotating coordinate system, the equations of motion in six degrees of freedom (6-DOF EOM) have a lot of partial derivatives. Look at the those equations and see if you have further questions. We are only allowed to give hints and direction for homework-type questions. You have to show us your work to get more help. (see this)

PS. Do not get discouraged if the equations seem overwhelming. Many of us, myself included, are still struggling with it.
 
Last edited:

Thread 'Does this series converge uniformly?'

First, I tried to show that ##f_n## converges uniformly on ##[0,2\pi]##, which is true since ##f_n \rightarrow 0## for ##n \rightarrow \infty## and ##\sigma_n=\mathrm{sup}\left| \frac{\sin\left(\frac{n^2}{n+\frac 15}x\right)}{n^{x^2-3x+3}} \right| \leq \frac{1}{|n^{x^2-3x+3}|} \leq \frac{1}{n^{\frac 34}}\rightarrow 0##. I can't use neither Leibnitz's test nor Abel's test. For Dirichlet's test I would need to show, that ##\sin\left(\frac{n^2}{n+\frac 15}x \right)## has partialy bounded sums...
View full post »

Similar threads

Calculating the partial derivative in polar coordinates
Replies
3
Views
3K
Finding the partial derivative from the given information
Replies
2
Views
2K
Partial derivative stationary point
Replies
3
Views
2K
Solving Partial Differential Equation
Replies
2
Views
1K
Confirm Limit Existence for Function f w/o Piecewise Def.
Replies
4
Views
2K
Problem about existence of partial derivatives at a point
Replies
3
Views
4K
Total derivative of a partial derivative
Replies
3
Views
4K
Partial derivative using differentials
Replies
5
Views
2K
Understanding Traffic Flow Equations: Integrals and Partial Derivatives
Replies
2
Views
2K
How do I use the chain rule for finding second-order partial derivatives?
Replies
13
Views
2K