<p align="right">Last Update: <font color="#4f81bd">December 18, 2024</font></p> ### Introduction to Dynamics ==**Dynamics**== is the study of the motion and forces that ==_cause_== objects and systems to move; it is the explanation for motion. ==**Dynamics**== is a subset of mechanics in which the physicist emphasizes why there is motion. ==Statics== is the study of forces without motion. In ==classical mechanics==, we are given an approximation of why something happens. Motions of the very large and very small objects need something besides classical mechanics. The "why" does not mean there isn’t any math. On the contrary, geometry becomes valuable when an object is moving at an angle to the force being applied. However, the math is not as "intense" as kinematics. Models will be central to explaining motion. Models will be proposed, the models are tested, then there is a determination whether or not the model needs to be adjusted. --- These are the three general steps to solving dynamics problems. 1. Describe motion 2. Choose a physical law 3. Apply the math --- ### ==History of Dynamics== - Galileo and Newton are two important figures in modern classical mechanics. We will use their ideas as a springboard to newer ideas regarding motion. However, they did not work in isolation. - Nicolaus Copernicus, a polish physicist in the 1500s, stated the sun is the center of our solar system. This counters Claudius Ptolemy, who stated the Earth is the center of our solar system. - Tycho Brahe (1600) Imperial mathematician, astronomical observations - Johannes Kepler (1609) Three laws of planetary motion. - Galileo Galilei (1610-1620) Turn telescope to heaven - Rene Descartes (1630-1644) Analytical geometry; developed coordinate system - Isaac Newton (1643-1727) In 1666, three statements of the laws of motion. - Leonhard Euler (1707-1783) Put laws into mathematics, taught torque and angular momentum - Joseph-Louis Lagrange (1788) Reformulation of mechanics using energy-work concept to lead to equations of motion without using kinematics. ### ==Derivative Notation== Newton used a dot notation to identify a function, $\dot{x}$. Lagrange used an $f'(x)$. Leibniz used $\frac{dy}{dx}$ as a notation. Leibniz introduced the integral symbol $\int$. ### Slide Deck <div style="position: relative; width: 100%; height: 0; padding-top: 56.2500%; padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden; border-radius: 8px; will-change: transform;"> <iframe loading="lazy" style="position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;" src="https://www.canva.com/design/DAGPwMO9xr0/D7zndQfo6jnsm2MYLfxSBA/view?embed" allowfullscreen="allowfullscreen" allow="fullscreen"> </iframe> </div> ### Related Topics --- [[Home|Home]] | [[Mechanics]] | [[Notes Vault/Physics Notes Vault/Kinematics/Kinematics|Kinematics]] | [[Notes Vault/Physics Notes Vault/Dynamics/Dynamics|Dynamics]] | [[Force]] | [[Net Force]] | [[Newton's First Law]] | [[Newton's Second Law]] | [[Newton's Third Law]] | [[Inertia]] | [[Notes Vault/Physics Notes Vault/Dynamics/Weight]] | [[Normal Forces]] | [[Notes Vault/Physics Notes Vault/Dynamics/Friction]]