Interactive Course Animations

Engineering Dynamics

Particle kinematics

1. Rectilinear motion with constant acceleration Interactive animation of constant-acceleration motion: position, velocity and acceleration linked on one timeline. Free, browser-based dynamics demo. Türkçe
2. Graphical method: shape the v–t graph yourself Interactive velocity-time graph animation: read displacement as area and acceleration as slope, live. Free browser-based dynamics course demo. Türkçe
3. Projectile motion Interactive projectile motion animation with launch angle and speed sliders: trajectory, range and apex computed live in your browser. Türkçe
4. Curvilinear motion: normal acceleration and curvature Interactive animation of curvilinear motion: normal and tangential acceleration components along a curved path, visualized live. Türkçe
5. Car on a banked curve Interactive banked curve animation: design speed, friction and bank angle on a curved road, with real examples from Daytona and railway cant. Türkçe
6. Polar coordinates and the Coriolis term Interactive polar coordinates animation: radial and transverse velocity and acceleration components of a particle, visualized live. Türkçe
7. Dependent motion: pulleys Interactive pulley-rope dependent motion animation: cable length constraints link the speeds of two blocks. Includes block-and-tackle examples. Türkçe
8. Relative motion: two aircraft Interactive relative motion animation: velocity of one moving object seen from another, with vector diagrams drawn live. Türkçe
9. Pursuit curve: pure pursuit vs intercept (advanced) Interactive pursuit curve animation: a chaser always aiming at a moving target, with links to pursuit and proportional navigation guidance. Türkçe
10. Circular pursuit: the n-bug problem (advanced) Interactive mice problem animation: n pursuers chasing each other into logarithmic spirals, after Lucas (1877). Browser-based dynamics demo. Türkçe
11. Transition curves: the clothoid and lateral jerk (advanced) Interactive clothoid (Euler spiral) animation: why road and roller-coaster transition curves ramp curvature linearly. Free browser demo. Türkçe
12. 3D helix and the Frenet frame (advanced) Interactive helix animation with Frenet frame: tangent, normal and binormal vectors on a 3D spiral path, with parking-ramp examples. Türkçe
13. Satellite in polar coordinates: Kepler’s second law Radial and transverse velocity on an elliptical orbit; equal-area sectors show why constant areal rate means the force is central. Türkçe
14. The parabola of safety: the envelope of all trajectories (advanced) Torricelli’s boundary between reachable and safe; every interior target takes exactly two launch angles, the envelope takes one. Türkçe

Particle kinetics

0. Air Track: Newton’s Laws of Motion Interactive air track animation: one push reveals the first law, a rubber band at constant stretch draws the straight v–t line of the second, and mass is defined by the experiment itself. Türkçe
1. Brachistochrone race: which slide is fastest? Interactive brachistochrone race animation: straight ramp vs circular arc vs cycloid, which slide is fastest and why. Verified physics. Türkçe
2. Box on a conveyor belt: friction, slip and heat Interactive conveyor belt friction animation: box slip time, friction heat and motor work, with a live velocity-time graph. Türkçe
3. The Gravitron: pinned to the wall by friction Interactive Gravitron rotor ride animation: the friction and normal force that pin riders to the wall, with the minimum-speed threshold. Türkçe
4. Hill and loop: energy conservation and the normal force Interactive vertical loop animation: energy conservation, normal force and the 2.5R minimum height rule for completing the loop. Türkçe
5. Crumple zones and airbags: stretching the impulse Interactive crash impulse animation: dashboard vs seat belt vs airbag, same momentum change spread over longer times and lower forces. Türkçe
6. The bouncing ball and the coefficient of restitution Interactive bouncing ball animation: coefficient of restitution, bounce height decay and total bouncing time, with ITF tennis ball data. Türkçe
7. Newton's cannonball: from fall to orbit to escape Interactive Newton's cannonball animation: from falling shot to circular orbit to escape velocity, integrated live with real gravity. Türkçe
8. Puck on a shrinking string: angular momentum Interactive angular momentum animation: a puck on a shortening string spins faster, with the tension-radius curve and work-energy check. Türkçe
9. The ballistic pendulum: momentum, then energy Interactive ballistic pendulum animation: momentum conservation in the embed, energy conservation in the swing, after Robins (1742). Türkçe
10. Chain falling onto a scale: the factor of three (advanced) Interactive falling chain animation: why a chain landing on a scale reads three times the landed weight. Momentum flux made visible. Türkçe
11. The rocket equation and staging (advanced) Interactive Tsiolkovsky rocket equation animation: single stage vs two stages with the same propellant, and why rockets must stage. Türkçe
12. The gravity assist: stealing speed from a planet (advanced) Interactive gravity assist animation: a hyperbolic flyby in the planet frame vs the Sun frame, and where the stolen speed comes from. Türkçe
13. The Magnus effect: bending a free kick (advanced) Interactive Magnus effect animation: a spinning free kick bending around the wall, after Roberto Carlos 1997. Verified drag and lift model. Türkçe
14. The stratosphere jump: drag in a thinning atmosphere (advanced) Interactive stratosphere jump animation: supersonic free fall through a thinning atmosphere, modeled on Red Bull Stratos 2012. Türkçe

Rigid-body kinematics

1. The rolling wheel and the point that moves backward Interactive rolling wheel animation: cycloid paths, the instantaneous center and the train-wheel flange point that moves backward. Türkçe
2. Slider-crank: why inline-four engines buzz Interactive slider-crank animation: exact piston kinematics vs simple harmonic motion, and the inline-four secondary shaking force. Türkçe
3. Fixed-axis rotation: the bicycle drivetrain Interactive gear-ratio animation: one chain speed, two sprockets, v = ωr twice in a row and your road speed, live. Türkçe
4. Curvilinear translation: the locomotive side rod Interactive parallelogram-linkage animation: the coupler moves on circles with zero angular velocity — until one link length breaks the parallelogram. Türkçe
5. Sliding ladder: the instant center that will not sit still Interactive sliding ladder animation: the IC glides along a circle, the top end slams down as the ladder flattens, and why the IC is a velocity tool only. Türkçe
6. Four-bar linkage: the windshield wiper Interactive crank-rocker animation: relative velocity arrows drawn live, Grashof’s condition and the transmission angle that decides smooth running. Türkçe
7. Cam and follower: designing motion itself Interactive cam animation: uniform, harmonic and cycloidal laws, live s–v–a diagrams, and acceleration that scales with speed squared. Türkçe
8. Quick-return mechanism: Coriolis on the shop floor Interactive crank and slotted lever animation: a 1.71 time ratio from one constant-speed crank, with the Coriolis arrow drawn on the sliding block. Türkçe
9. Planetary gears: one gearbox, three personalities Interactive epicyclic gear animation: the Willis equation, and fixing the ring, carrier or sun to get a reducer, a reverse and an overdrive. Türkçe
10. Geneva drive: the mechanism that made movies move Interactive Geneva drive animation: 24 frames per second, 10.4 ms of motion per index, and a film strip advancing frame by frame. Türkçe
11. The rolling cone: adding angular velocities in 3-D (advanced) Two angular velocity vectors add into one, the resultant lies along the contact line, and bevel gears fall out of the geometry. Türkçe
12. Gimbal lock: how Apollo almost lost its bearings (advanced) Three nested gimbals, the pitch-90 singularity where two axes align, and the fourth gimbal Apollo declined. Türkçe
13. Chasles’ theorem: every motion is a screw (advanced) Any rigid displacement equals one rotation about a line plus a slide along it — the clumsy two-step path versus the single helix. Türkçe
14. Quaternions: the fix for gimbal lock (advanced) One tumbling body, two bookkeepers: Euler-angle rates whip near the pole while the quaternion stays exact to 10⁻¹¹. Türkçe

Rigid-body kinetics

1. Why a falling chimney breaks in mid-air Interactive falling chimney animation: the bending moment that snaps tall structures near one third of their height, live. Türkçe
2. The skater and the pulsar Interactive angular momentum animation: a figure skater's spin and a collapsing star becoming a pulsar, one conservation law. Türkçe
3. The rolling race: hoop, disk, sphere Interactive rolling race animation: hoop, disk and sphere on an incline. Shape decides the winner; mass and radius cancel. Türkçe
4. The center of percussion: why bad hits sting Interactive sweet-spot animation: strike a pivoted bat and watch the hand reaction impulse flip sign and vanish at two thirds of the length. Türkçe
5. The bowling ball: sliding into rolling Interactive skid-to-roll animation: friction brakes and spins the ball until v = ωR, always at 5/7 of launch speed, 13.3 m down the lane. Türkçe
6. Gyroscopic precession: the wheel that refuses to fall Interactive gyroscope animation: M = dL/dt makes the spinning wheel orbit the pedestal, and faster spin means slower precession. Türkçe
7. The pulled spool: which way does it roll? Interactive spool paradox: the roll direction flips at the critical angle where the thread’s line of action passes through the contact point. Türkçe
8. The billiard strike: follow, draw and the 7R/5 rule Interactive cue ball animation: strike height sets the spin, and hitting at 7R/5 gives instant rolling with zero slide. Türkçe
9. Wheelies and stoppies: the weight-transfer limit Interactive motorcycle animation: wheel loads trade with acceleration until the front axle unloads at a = gb/h. Türkçe
10. The flywheel: storing energy in spin Interactive flywheel animation: 493 kJ at 60,000 rpm in a 5 kg disk, and the hoop-stress limit that forces carbon fiber and vacuum. Türkçe
11. The Dzhanibekov effect: the intermediate axis theorem (advanced) A T-handle flips end over end in orbit with no torque at all; Euler’s equations integrated live show why two axes are stable and one is not. Türkçe
12. Feynman’s wobbling plate: torque-free precession (advanced) The thrown cafeteria plate wobbles at twice its spin; the live counter measures the famous factor of two to three decimals. Türkçe
13. The heavy top: nutation and cusps (advanced) Release the gyroscope from rest and it dips, nods and precesses; the full equations draw the cusped path the simple formula hides. Türkçe
14. Rotor imbalance: forces growing with speed squared (advanced) Static versus couple unbalance, bearing forces as Uω², and the phase signature every balancing technician reads. Türkçe

Numerical Methods

Errors and floating-point arithmetic

1. The number line has gaps: floats, ulp and machine epsilon Interactive floating-point animation: the float number grid, ulp spacing and machine epsilon, with a single-precision clock that freezes. Türkçe
2. Catastrophic cancellation: measuring a strain Interactive catastrophic cancellation animation: subtracting nearly equal numbers destroys digits, shown on a strain measurement. Türkçe
3. Drift: the Patriot clock, 1991 Interactive rounding-error accumulation animation: the 1991 Patriot missile clock drift, 0.34 s in 100 hours, recomputed live. Türkçe

Root finding

4. Bisection vs Newton: the buckling load of a fixed-pinned column Interactive bisection vs Newton-Raphson animation on the column buckling equation tan(kL)=kL, with convergence rates and failure modes. Türkçe
5. The secant method fires back: finding the launch angle Interactive secant method animation: finding the launch angle of a drag-affected projectile, one cannon shot per iteration. Türkçe

Nonlinear systems

6. A four-bar linkage solved live by Newton–Raphson Interactive four-bar linkage animation: Newton-Raphson solves the loop-closure equations live every frame, with quadratic convergence and branch choice. Türkçe

Linear systems

7. Gaussian elimination and the pivot that saves it Wilkinson’s wartime desk-computer solve, elimination on a truss, and the small-pivot disaster that 3-digit arithmetic exposes. Türkçe
8. Condition number: why your GPS fails in a canyon Two nearly parallel lines, digits lost as logκ, and satellite geometry turning 1 m of range noise into 50 m of position error. Türkçe

Interpolation and curve fitting

9. Runge’s phenomenon: when more points make it worse The 1901 equispaced-polynomial disaster, Chebyshev nodes, and the cubic spline that lives inside every CAD kernel. Türkçe
10. Least squares: how Gauss found a lost planet Ceres 1801, residual squares you can watch shrink while fitting a modulus, and the degree-7 polynomial that memorizes and predicts nothing. Türkçe

Numerical integration and differentiation

11. Numerical integration: from Kepler’s wine barrel to crash energy The 1615 barrel rule that became Simpson’s, trapezoid vs parabolic panels on a crash curve, and measured convergence orders 2 and 4. Türkçe
12. Numerical differentiation: the step size dilemma The live V-curve where truncation meets roundoff, the √ε wall, and why half the machine’s digits are the best you can buy. Türkçe

Differential equations

13. The pendulum past 90°: Euler vs RK4 Interactive large-angle pendulum animation: Euler vs RK4 integration, energy drift and the exact elliptic-integral period, computed live. Türkçe
14. Heat in a bar and the step size that breaks it Interactive heat-conduction animation: the explicit FTCS finite-difference scheme blows up past r = 1/2 — von Neumann stability live. Türkçe