Find the equations of the trajectories?

In summary, finding the equations of trajectories is important for understanding the path or motion of an object in a given system. These equations can be determined using mathematical principles such as calculus and physics laws, and can be affected by factors such as initial conditions, external forces, and the nature of the system. They can be used for all types of motion and are crucial in scientific research for predicting and analyzing an object's behavior.
  • #1
Math10
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0

Homework Statement


Find the equations of the trajectories of y"+y^3=0.

Homework Equations


None.

The Attempt at a Solution


The Undamped Case:
y"+p(y)=0
v(dv/dy)+p(y)=0
integrate
v^2/2+P(y)=C
---------------------------------
So following the formula above:
The answer I got is v^2/2+y^4/4=C, but the answer in the book says v^2+y^4/4=C. What's wrong?
 
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  • #2
Did you, blindly, followed a formula?

What makes you think the formula applies in this case?
Did you follow the formula correctly?
Did you check your algebra?
Did you check your arithmetic?

Maybe the book made a typo?
 

Related to Find the equations of the trajectories?

1. What is the purpose of finding the equations of trajectories?

Finding the equations of trajectories is important for understanding the path or motion of an object in a given system. It can help predict the future position of the object and analyze its behavior.

2. How do you determine the equations of trajectories?

The equations of trajectories can be determined using mathematical principles such as calculus and physics laws like Newton's laws of motion. It involves analyzing the initial conditions, forces acting on the object, and solving differential equations.

3. What factors can affect the equations of trajectories?

The equations of trajectories can be affected by various factors such as the initial conditions, external forces, and the nature of the system. Other factors may include air resistance, friction, and other forms of resistance.

4. Can the equations of trajectories be used for all types of motion?

Yes, the equations of trajectories can be used for all types of motion, including linear, circular, and projectile motion. However, the specific equations and calculations may vary depending on the type of motion and the system being studied.

5. Why are the equations of trajectories important in scientific research?

The equations of trajectories are essential in scientific research because they allow for the accurate prediction and analysis of an object's motion. They also provide a mathematical basis for understanding the behavior of systems and can be used to make informed decisions in various fields such as physics, engineering, and astronomy.

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