[{"data":1,"prerenderedAt":44},["ShallowReactive",2],{"topic-en-theoretical-mechanics\u002Fdynamics\u002Fparticle-dynamics":3},{"topic":4,"trail":13,"children":23,"tasks":40,"alternates":41},{"id":5,"name":6,"locale":7,"path":8,"seo_title":6,"seo_description":9,"seo_text":10,"content_html":11,"content_chunks":12},293,"Particle Dynamics","en","theoretical-mechanics\u002Fdynamics\u002Fparticle-dynamics","Newton's laws, differential equations, fundamental dynamics problems, and particle motion under typical forces.","This section covers Newton's laws, differential equations of particle motion, the fundamental dynamics problems, and motion under typical forces.","\u003Cp>\u003Cstrong>Particle dynamics\u003C\u002Fstrong> establishes the relationship between particle motion and the forces acting on it. Unlike kinematics, acceleration is now interpreted as a consequence of force interaction according to Newton's laws.\u003C\u002Fp>\u003Ch2>Newton's laws\u003C\u002Fh2>\u003Cp>The section is based on inertia, the relation between resultant force and acceleration, and the action-reaction principle. For a particle of constant mass, the equation of motion is written in vector form and projected onto convenient axes.\u003C\u002Fp>\u003Ch2>Differential equations of motion\u003C\u002Fh2>\u003Cp>When forces are known as functions of position, velocity, or time, Newton's second law produces differential equations. Their solution together with initial conditions determines the particle's motion.\u003C\u002Fp>\u003Ch2>Direct and inverse problems\u003C\u002Fh2>\u003Cp>In one class of problems, a prescribed motion is used to determine the required force or resultant. In the other, known forces and initial conditions are used to determine motion. Typical models include gravity, elastic forces, and resistance.\u003C\u002Fp>",[],[14,18,22],{"id":15,"name":16,"path":17},81,"Theoretical Mechanics","theoretical-mechanics",{"id":19,"name":20,"path":21},138,"Dynamics","theoretical-mechanics\u002Fdynamics",{"id":5,"name":6,"path":8},[24,28,32,36],{"id":25,"name":26,"path":27},248,"Fundamental Laws of Dynamics. Newton's Laws","theoretical-mechanics\u002Fdynamics\u002Fparticle-dynamics\u002Ffundamental-laws-of-dynamics-newtons-laws",{"id":29,"name":30,"path":31},249,"Differential Equations of Motion of a Particle","theoretical-mechanics\u002Fdynamics\u002Fparticle-dynamics\u002Fdifferential-equations-of-motion-of-a-particle",{"id":33,"name":34,"path":35},250,"Two Fundamental Problems of Particle Dynamics","theoretical-mechanics\u002Fdynamics\u002Fparticle-dynamics\u002Ftwo-fundamental-problems-of-particle-dynamics",{"id":37,"name":38,"path":39},251,"Particle Motion Under Typical Forces","theoretical-mechanics\u002Fdynamics\u002Fparticle-dynamics\u002Fparticle-motion-under-typical-forces",[],{"en":42,"uk":43},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Ftopics\u002Ftheoretical-mechanics\u002Fdynamics\u002Fparticle-dynamics","https:\u002F\u002Fmechclassroom.com\u002Ftopics\u002Fteoretychna-mekhanika\u002Fdynamika\u002Fdynamika-materialnoi-tochky",1787712536955]