Classical Mechanics
Skills
Every skill in the course, and how you are doing on each.
Newtonian mechanics and conservation laws
- Drill
Homogeneous potential
- Drill
Fictitious potential
- Drill
Translation symmetry
- Drill
Velocity dependent force
- Drill
Jacobi integral
- Drill
Foucault pendulum
- Drill
Momentum constraint
- Drill
Relative acceleration
109 more topics with one problem
- Dimensional consistency
- Force law audit
- Galilean covariance
- Angular momentum balance
- Central pair force
- External torque
- Momentum coupling
- Moving origin
- Transport torque
- Endpoint correction
- Finite time virial
- Shifted equilibrium
- Translating frame
- Lagrangian energy balance
- Parametric power audit
- Time translation symmetry
- Collision invariants
- Energy frame shift
- Galilean boost
- Barycentric coordinates
- Origin independence
- Spin orbital split
- Accelerating stream
- Meshhersky equation
- Open system momentum
- Double well phase portrait
- Nonlinear stability
- Separatrix classification
- Elliptic integral asymptotics
- Pendulum quadrature
- Separatrix time divergence
- Equivalence principle
- Relative momentum
- Uniform body force
- Internal damping
- Momentum conservation
- Relative mode
- Jacobi coordinates
- Kinetic energy split
- Three body reduction
- Constraint impulse
- Inelastic capture
- Mass metric projection
- Accelerated frame invariant
- Pseudomomentum
- Uniform forcing
- Pair potential
- Rotation symmetry
- Time reversal
- Trajectory symmetry
- Energy preservation
- Skew coupling
- Continuous rotation
- Discrete symmetry
- Torque counterexample
- Lagrange jacobi identity
- N body inertia
- Coriolis euler centrifugal
- Rotation matrix theorem
- Time dependent frames
- Uniformly rotating frame
- Coriolis precession
- Latitude dependence
- Apparent weight
- Earth rotation
- Eotvos correction
- Inertia tensor rate
- Shape kinematics
- Tensor audit
- Internal couple
- Momentum versus angular
- Noncentral force
- Distributional impulse
- Momentum measure
- Velocity jump
- Gravity gradient torque
- Quadrupole moment
- Tidal orientation
- Damped phase contraction
- Drag history factor
- Nonautonomous flow jacobian
- Frame covariance
- Meshhersky balance
- Noninertial variable mass
- Collision jacobian
- Impact complementarity
- Restitution map
- Boost symmetry
- Center of mass integral
- Galilean charge
- Ideal rocket equation
- Mass allocation
- Staged rocket optimization
- Central configuration
- Euler collinear solution
- Three body rotation
- Harmonic trap
- Interaction independent frequency
- Kohn mode
- Breakup threshold
- Energy floor
- Bounded force
- Continuation bound
- Finite time blowup
- Energy rescaling
- N body scaling
- Newtonian similarity
- Accelerated frame equivalence
- Tidal curvature
Constraints and Lagrangian mechanics
- Drill
Routh reduction
- Drill
Canonical momentum
- Drill
Canonical angular momentum
- Drill
Frobenius test
- Drill
Second variation
- Drill
Singular lagrangian
109 more topics with one problem
- Cyclic angle
- Euler lagrange
- Polar coordinates
- Coordinate covariance
- Free particle
- Point coordinate
- Damped coordinate
- Power loss
- Rayleigh dissipation
- Inertial cross term
- Scale factor
- Time dependent coordinate
- Constraint reduction
- Generalized coordinate
- Track metric
- Cyclic moving support
- Pendulum cart coupling
- Mechanical momentum
- Translating coordinate
- Dimensional analysis
- Generalized force
- Virtual work
- Cyclic coordinates
- Cylinder geodesic
- Unwrapped path
- Constraint power
- Expanding circle
- Rheonomic constraint
- Azimuthal momentum
- Effective latitude
- Spherical pendulum
- Arc length coordinate
- Cycloid tautochrone
- Isochronous motion
- Effective gravity
- Moving support
- Pendulum lagrangian
- Cyclotron equation
- Symmetric gauge
- Velocity potential
- Azimuthal barrier
- Surface of revolution
- Equilibrium bifurcation
- Rotating hoop
- Coupled mass matrix
- Holonomic elimination
- Pulley network reduction
- Lagrange multiplier
- Normal reaction
- Plane constraint
- First integral
- Shifted momentum
- Time dependent force
- Conical pendulum
- Relative equilibrium
- Beltrami identity
- Brachistochrone
- Cycloid extremal
- Beltrami first integral
- Catenary
- Isoperimetric variation
- Great circle
- Sphere geodesic
- Vector multiplier
- Constraint reaction
- D alembert
- Nonholonomic knife edge
- Conical surface
- Routhian equilibrium
- Steady orbit
- Polar magnetic gauge
- Velocity dependent potential
- Boost integral
- Noether boundary term
- Quasi symmetry
- Horizontal drive
- Inertial torque
- Rheonomic pendulum
- Bilateral unilateral model boundary
- Constraint reaction interpretation
- Holonomic multiplier variation
- Ideal reaction
- Nonintegrable constraint
- Constrained stability
- Tangent curvature
- Fixed energy path
- Maupertuis principle
- Mechanical refraction
- Constraint tensions
- Coupled holonomic constraints
- Double pendulum multipliers
- Dependent equations
- Gauge freedom
- Fixed energy geometry
- Jacobi metric
- Turning boundary
- Dilation charge
- Inverse square potential
- Time scaling
- Caldirola kanai
- Canonical versus mechanical
- Damped action
- Ideal contact power
- Nonholonomic distribution
- Action extremum
- Conjugate point
- Gauge boundary term
- Moving magnetic constraint
- Reduced canonical momentum
Central-force motion and scattering
- Drill
Effective potential
- Drill
Angular momentum
- Drill
Orbital period
- Drill
Kepler energy
- Drill
Turning points
- Drill
Differential cross section
- Drill
Vis viva
- Drill
Kepler equation
- Drill
Time of flight
- Drill
Impact parameter
- Drill
Apsidal angle
- Drill
Radial action
96 more topics with one problem
- Central torque
- Orbital plane
- Central force
- Circular motion
- Radial sign
- Areal velocity
- Polar velocity
- Angular speed
- Kepler second law
- Specific angular momentum
- Centrifugal barrier
- Radial equation
- Flat rotation curve
- Logarithmic potential
- Energy threshold
- Escape speed
- Softened potential
- Barycentric frame
- Reduced mass
- Two body reduction
- Kepler conic
- Orbital elements
- Apsis classification
- Eccentricity
- State vector
- Hard sphere
- Specular reflection
- Apsides
- Orbital invariants
- True anomaly
- Epicyclic stability
- Marginal orbit
- Shifted potential
- Central scattering
- Closest approach
- Circular speed
- Screening limit
- Yukawa potential
- Epicyclic frequency
- Softened center
- Inverse orbit inference
- Power law stability
- Time average
- Virial theorem
- Apsidal precession
- Binet equation
- Inverse square correction
- Periapsis advance
- Resonant forcing
- Secular perturbation
- Composite potential
- Epicyclic motion
- Stability limits
- Newton iteration
- Orbital anomaly
- Deflection angle
- Hyperbolic flyby
- Apsis reconstruction
- Impulsive orbit change
- Adiabatic orbit
- Slow mass growth
- Linearized gravity
- Tidal tensor
- Adiabatic inspiral
- Dissipative orbit
- Energy angular momentum
- Hill equations
- Orbital epicycle
- Rotating frame
- Orbiting boundary
- Rainbow singularity
- Conical constraint
- Geometric precession
- Unrolled orbit
- Action angle
- Kepler degeneracy
- Coulomb orbit
- Impact jacobian
- Rutherford scattering
- Kepler symmetry
- Poisson algebra
- Runge lenz vector
- Collision regularization
- Kepler oscillator
- Levi civita map
- Critical impact
- Orbiting threshold
- Singular potential
- Beta function
- Finite time singularity
- Radial collapse
- Abel inversion
- Inverse scattering
- Weak deflection
- Barker equation
- Parabolic orbit
Small oscillations and normal modes
- Drill
Linearization
- Drill
Generalized eigenproblem
- Drill
Mass metric
- Drill
Effective stiffness
- Drill
Principal axes
- Drill
Circular polarization
- Drill
Mass defect
- Drill
Mode veering
- Drill
Gyroscopic stability
- Drill
Parametric instability
102 more topics with one problem
- Equilibrium curvature
- Stability
- Mode normalization
- Coordinate metric
- Linear order
- Nonlinear kinetic energy
- Geometric oscillator
- Holonomic constraint
- Small slope
- Kinetic coupling
- Positive definite
- Symmetric modes
- Internal vibration
- Zero mode
- Mode stability
- Stiffness hessian
- Sylvester criterion
- Centrifugal instability
- Rotating constraint
- Cyclic symmetry
- Degenerate modes
- Periodic ring
- Initial value
- Modal superposition
- Generalized modes
- Mass orthogonality
- Modal projection
- Center of mass
- Parity modes
- Triatomic chain
- Modal decoupling
- Proportional damping
- Rayleigh damping
- Mode ratio
- Rotational inertia
- Torsional modes
- Massless junction
- Static condensation
- Frequency estimate
- Rayleigh quotient
- Variational bound
- Discrete sine transform
- Finite chain
- Mode nodes
- Coriolis splitting
- Mixed coordinate modes
- Translation torsion
- Wilberforce oscillator
- Amended potential
- Radial mode
- Fixed chain
- Parity reduction
- Band gap
- Bloch dispersion
- Diatomic lattice
- Degenerate perturbation
- Frequency splitting
- Cantilever vibration
- Euler bernoulli beam
- Transcendental spectrum
- Complex modes
- Nonproportional damping
- Routh hurwitz
- Inverted oscillator
- Dynamic stabilization
- High frequency averaging
- Kapitza pendulum
- Design derivative
- Eigenvalue sensitivity
- Mass stiffness
- Double pendulum
- Modal synthesis
- Relative coordinates
- Action scaling
- Adiabatic invariant
- Slow parameter
- Floquet growth
- Mathieu equation
- Mode localization
- Surface mode
- Generalized spectral theorem
- Mass orthonormality
- Modal completeness
- Avoided crossing
- Mixing angle
- Dimerized chain
- Edge mode
- Topological localization
- Driven response
- Green matrix
- Modal resolvent
- Inverse eigenvalue
- Spectral design
- Spring network
- Degeneracy splitting
- Lindstedt expansion
- Nonlinear normal mode
- Balanced gain loss
- Exceptional point
- Quadratic pencil
- Floquet monodromy
- Switched oscillator
Rigid bodies and rotating frames
- Drill
Rolling sphere
- Drill
Euler equations
- Drill
Euler top
- Drill
Heavy symmetric top
- Drill
Cyclic momenta
- Drill
Rolling disk
- Drill
Angular impulse
- Drill
Heavy top
- Drill
Cyclic coordinate
96 more topics with one problem
- Inertia tensor
- Point mass system
- Rotational energy
- Axis shift
- Parallel axis tensor
- Thin ring
- Eigenvalue degeneracy
- Symmetric tensor
- Energy extrema
- Fixed angular momentum
- Inertia ellipsoid
- Angular momentum direction
- Energy angle
- Triaxial body
- Attitude kinematics
- Body components
- Euler angles
- Energy partition
- Principal moments
- Rotational kinetic energy
- Rotation matrix
- Torque frame transform
- Vector components
- Body frame derivative
- Torque free motion
- Body precession
- Symmetric top
- Conserved invariants
- Torque free proof
- Principal axis stability
- Fast slow branches
- Steady precession
- Nutation potential
- Compound angular velocity
- No slip kinematics
- Accelerating incline
- Static friction
- Center of percussion
- Pivot reaction
- Angular momentum exchange
- Internal actuation
- Reaction wheel
- Attitude matrix
- Noncommutativity
- Rotation composition
- Attitude update
- Constant angular velocity
- Quaternion kinematics
- Angular momentum ellipsoid
- Energy ellipsoid
- Poinsot construction
- Component bounds
- Invariant elimination
- Polhode
- Energy jump
- Principal inertia
- Hyperbolic map
- Intermediate axis
- Linearized flow
- Euler angle lagrangian
- Sleeping top
- Small tilt
- Nonholonomic constraint
- Contact velocity
- Rotating surface
- Euler invariants
- Growth rate
- Intermediate axis instability
- Complex phasors
- Rotor unbalance
- Two plane balancing
- Gravity gradient
- Satellite attitude
- Small libration
- Contact effective mass
- Restitution
- Rigid impact
- Elliptic integral
- Euler top quadrature
- Invariant reduction
- Dzhanibekov flip
- Logarithmic delay
- Separatrix solution
- Double root
- Heavy top separatrix
- Attitude control
- Bang bang maneuver
- Contact curvature
- Rocking frequency
- Rolling stability
- Effective mass
- Normal impulse
- Rigid collision
- Linear angular impulse
- Offset thruster
- Spacecraft dynamics
Hamiltonian mechanics and canonical structure
- Drill
Poisson bracket
- Drill
Hamilton flow
- Drill
Canonical scaling
- Drill
Symplectic map
- Drill
Rotating hamiltonian
- Drill
Phase area
- Drill
Leapfrog integrator
- Drill
Time dependent oscillator
89 more topics with one problem
- Hamiltonian energy
- Legendre transform
- Regular lagrangian
- Hamilton equations
- Harmonic oscillator
- Phase flow
- Action area
- Energy ellipse
- Phase portrait
- Canonical coordinates
- Leibniz rule
- Oscillator
- Poisson evolution
- Time dependent invariant
- Polar hamiltonian
- Liouville area
- Phase divergence
- Dimensionless variables
- Canonical map
- Generating function
- Momentum shear
- Canonical chart
- Global invertibility
- Generator time term
- Moving frame
- Time dependent canonical map
- Angular momentum coupling
- Explicit time
- Hamiltonian energy balance
- Translating trap
- Angular momentum algebra
- Rotation generator
- Central force hamiltonian
- Circular orbit
- Area preservation
- Linear canonical map
- Symplectic matrix
- Infinitesimal generator
- Poisson flow
- Jacobi identity
- Poisson transport
- Hamiltonian divergence
- Liouville theorem
- Phase volume
- Action integral
- Pendulum separatrix
- Canonical normal modes
- Coupled oscillators
- Orthogonal transform
- Canonical shear
- Quadratic hamiltonian
- Stability condition
- Gauge covariance
- Magnetic hamiltonian
- Electromagnetic potentials
- Gauge generator
- Time dependent canonical
- Legendre regularity
- Curvilinear hamiltonian
- Kinetic metric
- Spherical coordinates
- Linear stability
- Energy drift
- Euler integrators
- Accelerating frame
- Time dependent generator
- Canonical flow
- Hamiltonian generator
- Phase rotation
- Auxiliary amplitude
- Ermakov invariant
- Canonical shear composition
- Trace stability
- Symplectic diagonalization
- Fundamental matrix
- Wronskian invariant
- Cr3bp
- Jacobi constant
- Cylindrical hamiltonian
- Magnetic bottle
- Euler angle hamiltonian
- Backward error
- Shadow hamiltonian
- Floquet map
- Kicked oscillator
- Trace criterion
- Canonical capstone
- Constant force
- Freely falling frame