Math Fundamentals for 2D Physics Engines

Essential math concepts for 2D physics engine development: linear algebra, calculus, torque, and more

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Linear algebra, calculus, Taylor series.

Key Physics Terms

Impulse: The product of force and the time it acts (force × time). Represents how much mass and velocity change.

Momentum: A physics term for the quantity of motion. Calculated by multiplying mass by velocity, measured in kg⋅m/s.

Damping: A force that resists motion, similar to friction.

Calculus

A concept devised by Isaac Newton.

Differentiation

Think of it as finding the slope at any arbitrary point on a function.

Differentiation - slope of tangent line

Power Rule

Power Rule

Quotient Rule

Quotient Rule

Product Rule

Product Rule

Chain Rule

Chain Rule

Derivatives of Exponential and Logarithmic Functions

Exponential/Log derivatives

Integration

Finding the signed area under a curve.

Integration - signed area

Torque

Calculated using the cross product of vectors.

Torque

Eigenvalues

Needed for 3D physics engines (related to axes of rotation).

Eigenvalues

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