https://gamesweetgame.com/en/tags/physics/Recent content in Physics on GameSweetGameHugo -- gohugo.ioenMon, 01 Jan 2024 00:00:00 +0900https://gamesweetgame.com/en/p/math-fundamentals-for-2d-physics-engines/Mon, 01 Jan 2024 00:00:00 +0900https://gamesweetgame.com/en/p/math-fundamentals-for-2d-physics-engines/<p>Drawing with D2D.</p> <p>Linear algebra, calculus, Taylor series.</p> <h2 id="key-physics-terms">Key Physics Terms </h2><p><strong>Impulse:</strong> The product of force and the time it acts (force × time). Represents how much mass and velocity change.</p> <p><strong>Momentum:</strong> A physics term for the quantity of motion. Calculated by multiplying mass by velocity, measured in kg⋅m/s.</p> <p><strong>Damping:</strong> A force that resists motion, similar to friction.</p> <h2 id="calculus">Calculus </h2><p>A concept devised by Isaac Newton.</p> <h3 id="differentiation">Differentiation </h3><p>Think of it as finding the slope at any arbitrary point on a function.</p> <p><img alt="Differentiation - slope of tangent line" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px"></p> <h4 id="power-rule">Power Rule </h4><p><img alt="Power Rule" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px"></p> <h4 id="quotient-rule">Quotient Rule </h4><p><img alt="Quotient Rule" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px"></p> <h4 id="product-rule">Product Rule </h4><p><img alt="Product Rule" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px"></p> <h4 id="chain-rule">Chain Rule </h4><p><img alt="Chain Rule" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px"></p> <h4 id="derivatives-of-exponential-and-logarithmic-functions">Derivatives of Exponential and Logarithmic Functions </h4><p><img alt="Exponential/Log derivatives" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px"></p> <h3 id="integration">Integration </h3><p>Finding the signed area under a curve.</p> <p><img alt="Integration - signed area" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px"></p> <h2 id="torque">Torque </h2><p>Calculated using the cross product of vectors.</p> <p><img alt="Torque" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px"></p> <h2 id="eigenvalues">Eigenvalues </h2><p>Needed for 3D physics engines (related to axes of rotation).</p> <p><img alt="Eigenvalues" loading="lazy" sizes="(max-width: 767px) calc(100vw - 30px), (max-width: 1023px) 700px, (max-width: 1279px) 950px, 1232px"></p>