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

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SUMMARY

The discussion centers on the application of partial derivatives in calculating the acceleration of a car and analyzing projectile motion. Key examples include the Schrödinger equation and rocket flight, emphasizing the need to account for changes in both velocity and mass. The conversation highlights the importance of using rotating coordinate systems to analyze forces acting on an aircraft, such as engine forces, gravity, and aerodynamic forces, which all involve partial derivatives. The equations of motion in six degrees of freedom (6-DOF EOM) are also noted for their complexity and reliance on partial derivatives.

PREREQUISITES
  • Understanding of partial derivatives in calculus
  • Familiarity with the Schrödinger equation
  • Knowledge of six degrees of freedom (6-DOF) equations of motion
  • Basic principles of aerodynamics and forces acting on aircraft
NEXT STEPS
  • Study the application of partial derivatives in the Schrödinger equation
  • Research the equations of motion in six degrees of freedom (6-DOF EOM)
  • Explore the relationship between mass, velocity, and acceleration in rocket flight
  • Learn about rotating coordinate systems in physics and their impact on force analysis
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Students and professionals in physics, aerospace engineering, and applied mathematics who are interested in the practical applications of partial derivatives in motion analysis.

nrsakinh
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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
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my group is preferring the ue of partial derivative to find the acceleration of a car or the projectile motion of something being launched
 
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Have you heard of the Schrödinger 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.
 
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