What's the best way to choose a mathematical model for your mechanics problem?

1 Identify your objectives

Before you start modeling, you need to have a clear idea of what you want to achieve with your model. What are the main questions or goals you have for your problem? What are the relevant variables or parameters you need to measure or estimate? What are the expected outcomes or results you want to obtain or compare? By defining your objectives, you can narrow down the type and scope of your model, and avoid unnecessary complexity or confusion.

2 Review existing models

You don't have to reinvent the wheel every time you face a mechanics problem. Chances are, someone else has already developed a model that is similar or applicable to your problem, or at least to some aspects of it. You can review existing models from textbooks, journals, websites, or software libraries, and see how they approach your problem, what assumptions they make, what equations they use, and how they validate their results. You can also learn from their strengths and weaknesses, and see if you can adapt or improve their models for your problem.

3 Choose the appropriate level of abstraction

One of the key decisions you have to make when choosing a mathematical model is how much detail or realism you want to include in your model. This depends on the level of abstraction you choose for your model, which is the degree of simplification or generalization you apply to your problem. A higher level of abstraction means a more simplified model, which is easier to formulate and solve, but may not capture all the relevant features or effects of your problem. A lower level of abstraction means a more realistic model, which is more accurate and comprehensive, but may also be more complex and computationally demanding. You have to balance the trade-off between simplicity and realism, and choose the level of abstraction that suits your objectives and resources.

4 Validate and test your model

Once you have chosen a mathematical model for your problem, you have to make sure that it works as intended and produces reliable results. You can do this by validating and testing your model, which are two complementary processes that check the quality and performance of your model. Validation is the process of comparing your model results with experimental data or other sources of evidence, to see if your model is consistent with reality. Testing is the process of applying your model to different scenarios or conditions, to see if your model is robust and sensitive to changes. By validating and testing your model, you can identify and correct any errors or limitations in your model, and increase your confidence and credibility in your model.

5 Communicate and document your model

The final step in choosing a mathematical model for your mechanics problem is to communicate and document your model, so that others can understand, use, or review your model. You can communicate your model by presenting your objectives, assumptions, equations, results, and conclusions in a clear and concise manner, using appropriate formats, such as graphs, tables, diagrams, or code. You can document your model by providing detailed and consistent information about your model, such as the sources, methods, parameters, and references you used, as well as the limitations, uncertainties, and recommendations you have for your model. By communicating and documenting your model, you can share your knowledge and insights, and contribute to the advancement of mechanics modeling and simulation.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?