# Solving Rocket Launch Differential Equations

• mysticboon
In summary, the conversation discusses the process of solving rocket launch differential equations to find the apogee of an orbit. The participant is struggling to work with the equations in MATLAB and is seeking help in simplifying and solving them numerically. The principles of Newton's second law are mentioned, and the use of the "ode45" function in MATLAB is recommended.
mysticboon
Hi I'm currently working on a project which involves solving the rocket launch differential equations to find the apogee of an orbit. I know the analytical model for the equations as:
Δu = Isp*g0*ln(mf/me), where Isp is fuel impusle, mf is mass of full tank and me is mass of empty tank, but for this project I need to solve the differential equations in MATLAB numerically.

I know the general equation as d(M*u)/dt = Fnet = Isp*g0*dmp/dt where dmp is the change in mass of the propellant. I'm just kind of stuck in working around the differential equations to get something I can solve for in matlab. I've tried substituting some differentials for each other in order to get one equation, but I ended up cancelling terms to get something that doesn't make sense to me. I've been using this site to work with the equations: http://exploration.grc.nasa.gov/education/rocket/rktpow.html
Code:
% Veq = Isp*g0
% mdot = F/(Isp*g0)
% mdot = dmp/dt
% Mdu = Veq*mdot
% dm = -dmp = -mdot = -F/(Isp*g0)
% dmp = fnet/veq = fnet/(Isp*go)
% du = -(Isp(g0)*fnet/(Isp*g0)/M
Can anyone please give me some help in how to get one or two differential equations to use in matlab? Thank you

Hello,

Thank you for reaching out for help with your project. Solving differential equations numerically in MATLAB can be a challenging task, but with the right approach, it can be done effectively.

First, it is important to understand the physical meaning behind the equations you are working with. The differential equations you have mentioned are based on the principles of Newton's second law, which states that the net force on an object is equal to its mass times its acceleration. In the context of rocket launches, this means that the force generated by the rocket's engine (Fnet) is equal to the change in momentum (M*u) over time.

To simplify the equations and make them more manageable, it can be helpful to rewrite the equations in terms of the rocket's mass instead of its momentum. This can be done using the relationship between momentum and mass, which is M*u = m*v, where m is the mass of the rocket and v is its velocity.

With this in mind, the differential equations you are working with can be rewritten as d(m*v)/dt = Fnet. This can be further simplified by breaking down the force (Fnet) into its components, which include the force of gravity, the force of drag, and the force generated by the rocket's engine.

Once you have a simplified equation in terms of the rocket's mass, you can then use MATLAB to solve it numerically. This can be done using the "ode45" function, which is designed specifically for solving ordinary differential equations. You will need to define the initial conditions (such as the initial mass, velocity, and acceleration) and the time interval over which you want to solve the equation.

I recommend checking out the documentation and examples for the "ode45" function to get a better understanding of how to use it. Additionally, you can also reach out to your peers or a professor for further assistance in using MATLAB to solve differential equations.

I hope this helps and best of luck with your project!

## 1. What are rocket launch differential equations?

Rocket launch differential equations are mathematical equations that describe the motion of a rocket during launch. They take into account factors such as gravity, air resistance, and thrust to predict the trajectory and velocity of the rocket.

## 2. Why is it important to solve rocket launch differential equations?

Solving rocket launch differential equations allows scientists and engineers to accurately predict the behavior of a rocket during launch. This information is crucial in designing and planning successful rocket launches.

## 3. What are some common methods used to solve these equations?

Some common methods used to solve rocket launch differential equations include numerical methods such as Euler's method and Runge-Kutta methods, as well as analytical methods such as Laplace transforms and series solutions.

## 4. How do initial conditions affect the solution of rocket launch differential equations?

Initial conditions, such as the rocket's starting position and velocity, have a significant impact on the solution of rocket launch differential equations. Small changes in these initial conditions can result in drastically different outcomes for the rocket's trajectory.

## 5. What are some challenges in solving rocket launch differential equations?

One challenge in solving rocket launch differential equations is accurately modeling the complex physics involved in rocket launches. Additionally, the equations may become more difficult to solve if additional factors, such as wind and atmospheric conditions, are included in the model.

• MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
1K
• MATLAB, Maple, Mathematica, LaTeX
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
1K
• Sci-Fi Writing and World Building
Replies
2
Views
2K
• Mechanics
Replies
37
Views
10K
• Introductory Physics Homework Help
Replies
10
Views
820
• Calculus and Beyond Homework Help
Replies
10
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Differential Equations
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
16
Views
1K