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Lesson 2 - Material Point and Rigid Body

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In order to simplify calculations in classical mechanics, real bodies are being substituted with their simplified models. Such models are Material Point and Rigid Body. All equations are based on these models. When you have a real object you need to simulate, you have to choose an appropriate model for it. There are no strict rules on how to do that, you just need to desire what model is most suitable for your case.

Material Point

Material Point model is used when you consider a motion of a system as a one single unit. The whole your system can be presented with a single point, which is inextricably linked with the system. We assume that the whole mass of the system is concentrated in this single point (this is typically a Center of Mass). The rotation of this point is not considered, only a translational motion. For instance, a spaceship is a complex system, which contains many modules interacting with each other somehow. However, when we only consider an orbital motion of a spaceship - we are interested in such things as current position and velocity. Therefore, all the internal complexity can be omitted and the whole spaceship can be considered as a material point.

Absolutely Rigid Body

This model is used when we are interested in more detailed motion investigation, when rotation is also considered. "Absolutely rigid" means that we don't take into account body deformation and treat it as rigid. In real world all bodies are flexible, even hard ones. However, for most practical tasks we can neglect small deformations and consider the system as a rigid body. For instance, if we are investigating a drifting motion of a sports car, using a material point model becomes a bad choice, since it can't capture car's rotation in horizontal plane. It should be treated as a rigid body. On the other hand, if the car is just moving straightforward and starts braking, and all we need is to estimate the braking distance - we can handle it with material point model. So, the choice is up to you!

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fig. 1.2.1 Material Point example

Material Point model is used here since we are investigating vehicles positions in global coordinate system (CS).

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fig. 1.2.2 Rigid Body example

Here we are exploring vehicle's force impact on the lift. Car's size is comparable with the lift's size and the contact between them occurs in 4 points (wheels). Therefore, Rigid Body Model is used in order to capture the correct force distribution along the lift.

These "models" we are talking about are just abstract concepts. They are influencing the set of equations we choose to compute the system. We will learn during this course how to compose and solve such equations.

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