Polynomial Fit in Python with NumPy
Florian Trautweiler, Towards Data Science
When it comes to understanding the world around us, few things are more fascinating than the physics of motion. Imagine throwing a ball into the air, watching it soar and fall, all while tracking its path with real-time data on position, velocity, and acceleration. This was the premise of a previous project I undertook, and I decided to take it a step further by predicting its trajectory using a simple physics model. In this article, I’ll share the process of fitting that model to the measured state of the ball and visualizing its predicted path.
The Physics of the Ball’s Motion
To start, let’s break down the physics model for our ball. For simplicity’s sake, I’ve focused exclusively on its vertical movement, turning a complex scenario into a one-dimensional problem. If you’ve ever tossed a ball yourself, you likely haven’t thought about air resistance in the moment—neither did I. Instead, I modeled the motion simply using the force of gravity, which acts consistently on the ball as it ascends and descends.
The only factor at play here is the gravitational acceleration, roughly 9.8 m/s². This gravitational force acts on the mass of the ball, pulling it downward as it rises.
Visualizing the Data
In my previous work, I created a real-time visualization of the ball’s trajectory. Here’s a glimpse of those impressive visuals:
Position, Velocity, and Acceleration Plots with Prediction
When it comes to visualizing this data, Python’s NumPy library is an excellent tool. It allows us to fit a polynomial to our data, which smoothens the trajectory and enables predictions based on previously gathered information.
Step-by-Step Guide to Using Polynomial Fit in Python
-
Data Collection: First, ensure you have your data—this could be in real-time or collected during a controlled experiment.
-
Model Selection: Choose an appropriate polynomial degree that strikes the right balance between underfitting and overfitting your data.
-
Fitting the Model: Use NumPy’s
polyfitfunction to fit the chosen polynomial to your data. This function returns the coefficients of the polynomial equation you can then use for predictions. - Visualizing the Fit: Finally, utilize visualization libraries like Matplotlib to plot your data and see the fitted polynomial curve overlaid on it.
Real-Life Application
Let me share a quick story to paint a clearer picture. Imagine a child tossing a ball at a local park in [your city’s favorite landmark, like Central Park or the Golden Gate Bridge]. As the ball ascends, it captures the attention of her friends, who cheer with every peak it reaches. By using the Python code I’ve outlined, anyone can analyze and predict those high-flying moments, giving insight into physics that can be both educational and fun.
Conclusion
The world of physics becomes more exciting when technology meets hands-on experimentation. By employing Python with NumPy for polynomial fitting, we can break down complex motions into understandable models, making learning about gravity and motion not just theoretical but highly engaging.
As we forge ahead in the realms of data analysis and predictive modeling, I look forward to witnessing the innovations that arise from integrating programming with physical sciences.
The AI Buzz Hub team is excited to see where these breakthroughs take us. Want to stay in the loop on all things AI? Subscribe to our newsletter or share this article with your fellow enthusiasts!
