The equation Pp + Qq + R is known asa)Charpits equationb)Lagranges equationc)Bernoullis equationd)Clairuts equationCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Option B is correct

Answer

Explanation:

Lagrange's Equation:
Lagrange's equation is a second-order ordinary differential equation used in classical mechanics to describe the motion of dynamical systems. The general form of Lagrange's equation is given by:
$$ \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q_i}} \right) - \frac{\partial L}{\partial q_i} = 0 $$
where $ L $ is the Lagrangian of the system, $ q_i $ are the generalized coordinates, and $ \dot{q_i} $ are the generalized velocities.

Given Equation:
The equation $ Pp + Qq + R $ is known as Lagrange's equation when it takes the form:
$$ P\dot{p} + Q\dot{q} + R = 0 $$
where $ p $ and $ q $ are the generalized coordinates, and $ P $, $ Q $, and $ R $ are constants.

Application:
Lagrange's equation is widely used in physics and engineering to analyze the motion of systems subject to constraints. It provides a powerful tool for deriving the equations of motion of complex mechanical systems, such as pendulums, vibrating systems, and celestial mechanics.

Conclusion:
In summary, the equation $ Pp + Qq + R $ is known as Lagrange's equation, which plays a crucial role in classical mechanics for describing the dynamics of physical systems.

Answer

Clairut's equation

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