Lagrangian mechanics - Quiz
A) James Clerk Maxwell B) Galileo Galilei C) Isaac Newton D) Joseph-Louis Lagrange
A) Thermal and Mechanical Energy B) Internal and External Energy C) Electrical and Magnetic Energy D) Kinetic and Potential Energy
A) Action B) Mass C) Reaction D) Force
A) Generalized Coordinates, their Time Derivatives, and Time B) Mass and Velocity C) Cartesian Coordinates and their Time Derivatives D) Potential Energy and Velocity
A) Dynamic Displacement B) Stationary Displacement C) Virtual Displacement D) Actual Displacement
A) Principle of Least Action B) Hooke's Law C) Newton's Second Law D) Ohm's Law
A) Generalized Coordinates B) Polar Coordinates C) Cartesian Coordinates D) Spherical Coordinates
A) Differential Equations B) Calculus of Variations C) Vector Calculus D) Linear Algebra
A) 1788 B) 1803 C) 1755 D) 1760
A) 9 B) N C) 6N D) 3N
A) Net force equals mass times acceleration for each particle. B) Momentum is always zero. C) Energy is conserved in all interactions. D) Force is inversely proportional to distance squared.
A) The kinetic energy B) The Hamiltonian C) The Lagrangian D) The force function
A) L = V - T B) L = 2T - V C) L = T - V D) L = T + V
A) T = (1/3) Σ from k=1 to N m_k v_k2 B) T = (1/2) Σ from k=1 to N m_k v_k2 C) T = Σ from k=1 to N m_k2 v_k D) T = Σ from k=1 to N m_k v_k
A) V = V(v1, v2, ...) B) Most generally, V = V(r1, r2, ..., v1, v2, ..., t) C) V remains constant D) V = V(r1, r2, ...)
A) No, only specific functions can be used B) Yes, in agreement with physical laws C) Only if it includes kinetic energy D) Only if it excludes potential energy
A) Rayleigh dissipation function B) Potential energy function C) Christoffel symbols D) Constraint equations
A) Dissipative forces B) Holonomic constraints C) Nonholonomic constraints D) Relativistic constraints
A) Constraints that are integrable B) Constraints with inequalities C) Constraints depending on particle velocities D) Constraints involving friction
A) μ = m1 * m2. B) μ = m1 - m2. C) μ = m1m2/(m1 + m2). D) μ = (m1 + m2)/2.
A) Single particle dynamics B) Multiparticle systems C) Conserved momenta D) Cyclic coordinates
A) Taylor expansion B) Legendre transformation C) Fourier transformation D) Laplace transformation
A) -∂V/∂x B) m x¨ C) m x˙ D) ∂L/∂x
A) 1708 B) 1755 C) 1788 D) 1743
A) R (center of mass position). B) r (radial distance). C) θ (theta). D) V (potential energy).
A) No, it is not gauge invariant. B) It depends on the specific system. C) Gauge invariance does not apply to canonical momentum. D) Yes, it is gauge invariant.
A) Kinetic energy (1/2)mv² B) Linear momentum pr C) Potential energy V(r) D) Angular momentum pφ
A) They are curved paths B) They are non-linear acceleration paths C) They are straight lines D) They represent maximum energy trajectories
A) The curl operator B) A scalar potential C) The gradient operator D) The divergence operator
A) φ B) m C) r D) θ
A) Variational principle violation B) Relativistic inconsistency C) Hamiltonian complexity D) Ostrogradsky instability
A) Only the applied non-constraint forces. B) Both constraint and non-constraint forces. C) Constraint forces only. D) Potential energy changes.
A) The Planck constant B) The speed of light C) Boltzmann constant D) Gravitational constant
A) Extremal trajectories or paths B) Paths with maximum energy C) Curved paths in spacetime D) Non-linear acceleration paths
A) mgy_pend B) Mgy_pend C) (1/2)mgy_pend2 D) mgx_pend
A) Free particles deviate from geodesics due to forces B) Newton's second law is unrelated to geodesics C) Geodesics represent maximum force paths D) Free particles follow geodesics, which are extremal trajectories
A) The center-of-mass motion term. B) The potential energy due to the central force. C) The relative motion term. D) The total kinetic energy of the system.
A) -mr(θ̇² + sin²(θ)φ̇²) B) -m(r̈ + θ̇² + sin²(θ)φ̇²) C) m(r̈ - θ̇² - sin²(θ)φ̇²) D) mr(θ̇² + sin²(θ)φ̇²)
A) -mr²sin(θ)cos(θ)φ̇² B) m(r²θ̇ + sin(θ)cos(θ)φ̇) C) mr²sin(θ)cos(θ)φ̇² D) -mr²sin(θ)φ̇
A) ∇V B) m x˙ C) d/dt(∂L/∂x) D) -∂V/∂x
A) pφ = m(r² + θ² + φ²) B) pφ = m(r²θ̇ + sin(θ)φ̇) C) pφ = (m/2)r²sin(θ)φ̇ D) pφ = mr²sin²(θ)φ̇
A) Leonhard Euler B) Isaac Newton C) Jacques Bernoulli D) Joseph-Louis Lagrange
A) Electromagnetism B) Quantum mechanics C) Thermodynamics D) Optics
A) The principle is only valid for linear systems. B) It can only be applied to static equilibrium. C) The displacements might be connected by a constraint equation. D) It requires knowledge of all forces acting on the system.
A) Ostrogradsky mechanics B) Routhian mechanics C) Relativistic mechanics D) Momentum space formulation
A) Noether's theorem B) Lagrange's theorem C) Newton's theorem D) Euler's theorem
A) Routhian mechanics B) Hamiltonian mechanics C) Optics D) Momentum space formulation
A) (d/dt)(∂L'/∂Qi) = Σj λj (∂ϕ'j/∂Q̇i). B) (d/dt)(∂L'/∂Q̇i) = ∂L'/∂Qi + Σj λj (∂ϕ'j/∂Qi). C) (d/dt)(∂L/∂q̇i) = ∂L/∂qi. D) (d/dt)(∂L'/∂Qi) = ∂L'/∂Q̇i + Σj λj (∂ϕ'j/∂Q̇i).
A) Fcf = μrθ˙² = ℓ²/(μr³). B) Fcf = μr²θ˙. C) Fcf = μr/θ˙. D) Fcf = dV/dr. |
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